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py-why/dowhy

Revise user guide entry for intrinsic causal influence

2023-02-24 21:36:44+00:00

2023-03-07 16:13:45+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/quantify_intrinsic_causal_influence.rst

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic influence on the target node. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data. >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> from dowhy.gcm.uncertainty import estimate_variance >>> np.random.seed(10) # to reproduce these results >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we will model cause-effect relationships as a structural causal model and fit it to the data. >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, data) .. Todo: Use auto module for automatic assignment! Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> gcm.ml.create_linear_regressor(), >>> lambda x, _: estimate_variance(x)) >>> contributions {'X': 33.34300732332951, 'Y': 9.599478688607254, 'Z': 0.9750701113403872} **Interpreting the results:** We estimated the intrinsic influence of ancestors of :math:`Z`, including itself, to its variance. These contributions sum up to the variance of :math:`Z`. We observe that ~76% of the variance of :math:`Z` comes from :math:`X`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Consider the following example to get the intuition behind the notion of "intrinsic" causal influence we seek to measure here. A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the `intrinsic causal influence <https://arxiv.org/pdf/2007.00714.pdf>`_ of a source node to a target node, we need a functional causal model. In particular, we assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. entropy, variance) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> lambda x, _: estimate_variance(x)) .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the uncertainty estimator with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". .. Todo: Add this once confidence intervals is added! Above, we report point estimates of Shapley values from a sample drawn from the estimated joint distribution :math:`\hat{P}_{X, Y, Z}`. To quantify the uncertainty of those point estimates, we now compute their `bootstrap confidence intervals <https://ocw.mit .edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings /MIT18_05S14_Reading24.pdf>`_ by simply running the above a number of times, and aggregating the results. >>> from gcm import confidence_intervals, bootstrap_sampling >>> >>> node_to_mean_contrib, node_to_contrib_conf = confidence_intervals( >>> bootstrap_sampling(gcm.intrinsic_causal_influence, causal_model, 'Z', >>> prediction_model_from_noises_to_target, lambda x, _: estimate_variance(x)), >>> confidence_level=0.95, >>> num_bootstrap_resamples=200) Note that the higher the number of repetitions, the better we are able to approximate the sampling distribution of Shapley values.

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic causal influence on the target node. This method is based on the paper: Dominik Janzing, Patrick Blöbaum, Lenon Minorics, Philipp Faller, Atalanti Mastakouri. `Quantifying intrinsic causal contributions via structure preserving interventions <https://arxiv.org/abs/2007.00714>`_ arXiv:2007.00714, 2021 Let's consider an example from the paper to understand the type of influence being measured here. Imagine a schedule of three trains, ``Train A, Train B`` and ``Train C``, where the departure time of ``Train C`` depends on the arrival time of ``Train B``, and the departure time of ``Train B`` depends on the arrival time of ``Train A``. Suppose ``Train A`` typically experiences much longer delays than ``Train B`` and ``Train C``. The question we want to answer is: How strong is the influence of each train on the delay of ``Train C``? While there are various definitions of influence in the literature, we are interested in the *intrinsic causal influence*, which measures the influence of a node that has not been inherited from its parents, that is, the influence of the noise of a node. The reason for this is that, while ``Train C`` has to wait for ``Train B``, ``Train B`` mostly inherits the delay from ``Train A``. Thus, ``Train A`` should be identified as the node that contributes the most to the delay of ``Train C``. See the :ref:`Understanding the method <understand-method>` section for another example and more details. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data following the example above: >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> X = abs(np.random.normal(loc=0, scale=5, size=1000)) >>> Y = X + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> Z = Y + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Note the larger standard deviation of the 'noise' in :math:`X`. Next, we will model cause-effect relationships as a structural causal model and fit it to the data. Here, we are using the auto module to automatically assign causal mechanisms: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> gcm.auto.assign_causal_mechanisms(causal_model, data) >>> gcm.fit(causal_model, data) Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z') >>> contributions {'X': 8.736841722582117, 'Y': 0.4491606897202768, 'Z': 0.35377942123477574} Note that, although we use a linear relationship here, the method can also handle arbitrary non-linear relationships. **Interpreting the results:** We estimated the intrinsic causal influence of ancestors of :math:`Z`, including itself, to its variance (the default measure). These contributions sum up to the variance of :math:`Z`. As we see here, we observe that ~92% of the variance of :math:`Z` comes from :math:`X`. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Let's look at a different example to explain the intuition behind the notion of "intrinsic" causal influence further: A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the intrinsic causal influence of a source node to a target node, we need a functional causal model. For instance, we can assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. variance or entropy) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=lambda x, _: estimate_variance(x)) Here, we explicitly defined the variance in the parameter ``attribution_func`` as the property we are interested in. .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the ``attribution_func`` with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". **Remark on using the mean for the attribution:** Although the ``attribution_func`` can be customized for a given use case, not all definitions make sense. For instance, using the **mean** does not provide any meaningful results. This is because the way influences are estimated is based on the concept of Shapley values. To understand this better, we can look at a general property of Shapley values, which states that the sum of Shapley values, in our case the sum of the attributions, adds up to :math:`\nu(T) - \nu(\{\})`. Here, :math:`\nu` is a set function (in our case, the expectation of the ``attribution_func``), and :math:`T` is the full set of all players (in our case, all noise variables). Now, if we use the mean, :math:`\nu(T)` becomes :math:`\mathbb{E}_\mathbf{N}[\mathbb{E}[Y | \mathbf{N}]] = \mathbb{E}[Y]`, because the target variable :math:`Y` depends deterministically on all noise variables :math:`\mathbf{N}` in the graphical causal model. Similarly, :math:`\nu(\{\})` becomes :math:`\mathbb{E}[Y | \{\}] = \mathbb{E}[Y]`. This would result in :math:`\mathbb{E}_\mathbb{N}[\mathbb{E}[Y | \mathbb{N}]] - \mathbb{E}[Y | \{\}] = 0`, i.e. the resulting attributions are close to 0. For more details, see Section 3.3 of the paper.

bloebp

a1dcccbc805cb28aa4840fe9bce8338278632a50

12168ea7bd7a30d4c0d6501f69c7161ddb073845

We did not explain "simple linear relationship" before this text.

kailashbuki

py-why/dowhy

Revise user guide entry for intrinsic causal influence

2023-02-24 21:36:44+00:00

2023-03-07 16:13:45+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/quantify_intrinsic_causal_influence.rst

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic influence on the target node. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data. >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> from dowhy.gcm.uncertainty import estimate_variance >>> np.random.seed(10) # to reproduce these results >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we will model cause-effect relationships as a structural causal model and fit it to the data. >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, data) .. Todo: Use auto module for automatic assignment! Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> gcm.ml.create_linear_regressor(), >>> lambda x, _: estimate_variance(x)) >>> contributions {'X': 33.34300732332951, 'Y': 9.599478688607254, 'Z': 0.9750701113403872} **Interpreting the results:** We estimated the intrinsic influence of ancestors of :math:`Z`, including itself, to its variance. These contributions sum up to the variance of :math:`Z`. We observe that ~76% of the variance of :math:`Z` comes from :math:`X`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Consider the following example to get the intuition behind the notion of "intrinsic" causal influence we seek to measure here. A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the `intrinsic causal influence <https://arxiv.org/pdf/2007.00714.pdf>`_ of a source node to a target node, we need a functional causal model. In particular, we assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. entropy, variance) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> lambda x, _: estimate_variance(x)) .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the uncertainty estimator with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". .. Todo: Add this once confidence intervals is added! Above, we report point estimates of Shapley values from a sample drawn from the estimated joint distribution :math:`\hat{P}_{X, Y, Z}`. To quantify the uncertainty of those point estimates, we now compute their `bootstrap confidence intervals <https://ocw.mit .edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings /MIT18_05S14_Reading24.pdf>`_ by simply running the above a number of times, and aggregating the results. >>> from gcm import confidence_intervals, bootstrap_sampling >>> >>> node_to_mean_contrib, node_to_contrib_conf = confidence_intervals( >>> bootstrap_sampling(gcm.intrinsic_causal_influence, causal_model, 'Z', >>> prediction_model_from_noises_to_target, lambda x, _: estimate_variance(x)), >>> confidence_level=0.95, >>> num_bootstrap_resamples=200) Note that the higher the number of repetitions, the better we are able to approximate the sampling distribution of Shapley values.

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic causal influence on the target node. This method is based on the paper: Dominik Janzing, Patrick Blöbaum, Lenon Minorics, Philipp Faller, Atalanti Mastakouri. `Quantifying intrinsic causal contributions via structure preserving interventions <https://arxiv.org/abs/2007.00714>`_ arXiv:2007.00714, 2021 Let's consider an example from the paper to understand the type of influence being measured here. Imagine a schedule of three trains, ``Train A, Train B`` and ``Train C``, where the departure time of ``Train C`` depends on the arrival time of ``Train B``, and the departure time of ``Train B`` depends on the arrival time of ``Train A``. Suppose ``Train A`` typically experiences much longer delays than ``Train B`` and ``Train C``. The question we want to answer is: How strong is the influence of each train on the delay of ``Train C``? While there are various definitions of influence in the literature, we are interested in the *intrinsic causal influence*, which measures the influence of a node that has not been inherited from its parents, that is, the influence of the noise of a node. The reason for this is that, while ``Train C`` has to wait for ``Train B``, ``Train B`` mostly inherits the delay from ``Train A``. Thus, ``Train A`` should be identified as the node that contributes the most to the delay of ``Train C``. See the :ref:`Understanding the method <understand-method>` section for another example and more details. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data following the example above: >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> X = abs(np.random.normal(loc=0, scale=5, size=1000)) >>> Y = X + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> Z = Y + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Note the larger standard deviation of the 'noise' in :math:`X`. Next, we will model cause-effect relationships as a structural causal model and fit it to the data. Here, we are using the auto module to automatically assign causal mechanisms: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> gcm.auto.assign_causal_mechanisms(causal_model, data) >>> gcm.fit(causal_model, data) Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z') >>> contributions {'X': 8.736841722582117, 'Y': 0.4491606897202768, 'Z': 0.35377942123477574} Note that, although we use a linear relationship here, the method can also handle arbitrary non-linear relationships. **Interpreting the results:** We estimated the intrinsic causal influence of ancestors of :math:`Z`, including itself, to its variance (the default measure). These contributions sum up to the variance of :math:`Z`. As we see here, we observe that ~92% of the variance of :math:`Z` comes from :math:`X`. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Let's look at a different example to explain the intuition behind the notion of "intrinsic" causal influence further: A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the intrinsic causal influence of a source node to a target node, we need a functional causal model. For instance, we can assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. variance or entropy) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=lambda x, _: estimate_variance(x)) Here, we explicitly defined the variance in the parameter ``attribution_func`` as the property we are interested in. .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the ``attribution_func`` with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". **Remark on using the mean for the attribution:** Although the ``attribution_func`` can be customized for a given use case, not all definitions make sense. For instance, using the **mean** does not provide any meaningful results. This is because the way influences are estimated is based on the concept of Shapley values. To understand this better, we can look at a general property of Shapley values, which states that the sum of Shapley values, in our case the sum of the attributions, adds up to :math:`\nu(T) - \nu(\{\})`. Here, :math:`\nu` is a set function (in our case, the expectation of the ``attribution_func``), and :math:`T` is the full set of all players (in our case, all noise variables). Now, if we use the mean, :math:`\nu(T)` becomes :math:`\mathbb{E}_\mathbf{N}[\mathbb{E}[Y | \mathbf{N}]] = \mathbb{E}[Y]`, because the target variable :math:`Y` depends deterministically on all noise variables :math:`\mathbf{N}` in the graphical causal model. Similarly, :math:`\nu(\{\})` becomes :math:`\mathbb{E}[Y | \{\}] = \mathbb{E}[Y]`. This would result in :math:`\mathbb{E}_\mathbb{N}[\mathbb{E}[Y | \mathbb{N}]] - \mathbb{E}[Y | \{\}] = 0`, i.e. the resulting attributions are close to 0. For more details, see Section 3.3 of the paper.

bloebp

a1dcccbc805cb28aa4840fe9bce8338278632a50

12168ea7bd7a30d4c0d6501f69c7161ddb073845

Nit [for consistency reason]: intrinsic causal influence

kailashbuki

py-why/dowhy

Revise user guide entry for intrinsic causal influence

2023-02-24 21:36:44+00:00

2023-03-07 16:13:45+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/quantify_intrinsic_causal_influence.rst

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic influence on the target node. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data. >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> from dowhy.gcm.uncertainty import estimate_variance >>> np.random.seed(10) # to reproduce these results >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we will model cause-effect relationships as a structural causal model and fit it to the data. >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, data) .. Todo: Use auto module for automatic assignment! Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> gcm.ml.create_linear_regressor(), >>> lambda x, _: estimate_variance(x)) >>> contributions {'X': 33.34300732332951, 'Y': 9.599478688607254, 'Z': 0.9750701113403872} **Interpreting the results:** We estimated the intrinsic influence of ancestors of :math:`Z`, including itself, to its variance. These contributions sum up to the variance of :math:`Z`. We observe that ~76% of the variance of :math:`Z` comes from :math:`X`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Consider the following example to get the intuition behind the notion of "intrinsic" causal influence we seek to measure here. A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the `intrinsic causal influence <https://arxiv.org/pdf/2007.00714.pdf>`_ of a source node to a target node, we need a functional causal model. In particular, we assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. entropy, variance) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> lambda x, _: estimate_variance(x)) .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the uncertainty estimator with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". .. Todo: Add this once confidence intervals is added! Above, we report point estimates of Shapley values from a sample drawn from the estimated joint distribution :math:`\hat{P}_{X, Y, Z}`. To quantify the uncertainty of those point estimates, we now compute their `bootstrap confidence intervals <https://ocw.mit .edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings /MIT18_05S14_Reading24.pdf>`_ by simply running the above a number of times, and aggregating the results. >>> from gcm import confidence_intervals, bootstrap_sampling >>> >>> node_to_mean_contrib, node_to_contrib_conf = confidence_intervals( >>> bootstrap_sampling(gcm.intrinsic_causal_influence, causal_model, 'Z', >>> prediction_model_from_noises_to_target, lambda x, _: estimate_variance(x)), >>> confidence_level=0.95, >>> num_bootstrap_resamples=200) Note that the higher the number of repetitions, the better we are able to approximate the sampling distribution of Shapley values.

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic causal influence on the target node. This method is based on the paper: Dominik Janzing, Patrick Blöbaum, Lenon Minorics, Philipp Faller, Atalanti Mastakouri. `Quantifying intrinsic causal contributions via structure preserving interventions <https://arxiv.org/abs/2007.00714>`_ arXiv:2007.00714, 2021 Let's consider an example from the paper to understand the type of influence being measured here. Imagine a schedule of three trains, ``Train A, Train B`` and ``Train C``, where the departure time of ``Train C`` depends on the arrival time of ``Train B``, and the departure time of ``Train B`` depends on the arrival time of ``Train A``. Suppose ``Train A`` typically experiences much longer delays than ``Train B`` and ``Train C``. The question we want to answer is: How strong is the influence of each train on the delay of ``Train C``? While there are various definitions of influence in the literature, we are interested in the *intrinsic causal influence*, which measures the influence of a node that has not been inherited from its parents, that is, the influence of the noise of a node. The reason for this is that, while ``Train C`` has to wait for ``Train B``, ``Train B`` mostly inherits the delay from ``Train A``. Thus, ``Train A`` should be identified as the node that contributes the most to the delay of ``Train C``. See the :ref:`Understanding the method <understand-method>` section for another example and more details. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data following the example above: >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> X = abs(np.random.normal(loc=0, scale=5, size=1000)) >>> Y = X + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> Z = Y + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Note the larger standard deviation of the 'noise' in :math:`X`. Next, we will model cause-effect relationships as a structural causal model and fit it to the data. Here, we are using the auto module to automatically assign causal mechanisms: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> gcm.auto.assign_causal_mechanisms(causal_model, data) >>> gcm.fit(causal_model, data) Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z') >>> contributions {'X': 8.736841722582117, 'Y': 0.4491606897202768, 'Z': 0.35377942123477574} Note that, although we use a linear relationship here, the method can also handle arbitrary non-linear relationships. **Interpreting the results:** We estimated the intrinsic causal influence of ancestors of :math:`Z`, including itself, to its variance (the default measure). These contributions sum up to the variance of :math:`Z`. As we see here, we observe that ~92% of the variance of :math:`Z` comes from :math:`X`. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Let's look at a different example to explain the intuition behind the notion of "intrinsic" causal influence further: A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the intrinsic causal influence of a source node to a target node, we need a functional causal model. For instance, we can assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. variance or entropy) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=lambda x, _: estimate_variance(x)) Here, we explicitly defined the variance in the parameter ``attribution_func`` as the property we are interested in. .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the ``attribution_func`` with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". **Remark on using the mean for the attribution:** Although the ``attribution_func`` can be customized for a given use case, not all definitions make sense. For instance, using the **mean** does not provide any meaningful results. This is because the way influences are estimated is based on the concept of Shapley values. To understand this better, we can look at a general property of Shapley values, which states that the sum of Shapley values, in our case the sum of the attributions, adds up to :math:`\nu(T) - \nu(\{\})`. Here, :math:`\nu` is a set function (in our case, the expectation of the ``attribution_func``), and :math:`T` is the full set of all players (in our case, all noise variables). Now, if we use the mean, :math:`\nu(T)` becomes :math:`\mathbb{E}_\mathbf{N}[\mathbb{E}[Y | \mathbf{N}]] = \mathbb{E}[Y]`, because the target variable :math:`Y` depends deterministically on all noise variables :math:`\mathbf{N}` in the graphical causal model. Similarly, :math:`\nu(\{\})` becomes :math:`\mathbb{E}[Y | \{\}] = \mathbb{E}[Y]`. This would result in :math:`\mathbb{E}_\mathbb{N}[\mathbb{E}[Y | \mathbb{N}]] - \mathbb{E}[Y | \{\}] = 0`, i.e. the resulting attributions are close to 0. For more details, see Section 3.3 of the paper.

bloebp

a1dcccbc805cb28aa4840fe9bce8338278632a50

12168ea7bd7a30d4c0d6501f69c7161ddb073845

In that case, we would also need to introduce something like ``Y = max(0, X) + N``, since the following train will not leave earlier if the train is faster. I am not sure if we really need to make it that complicated here in the "how to use the method" section, since this is mostly to show how the API works? I only tried to link it a bit to the previous example to not have it completely abstract.

bloebp

py-why/dowhy

Revise user guide entry for intrinsic causal influence

2023-02-24 21:36:44+00:00

2023-03-07 16:13:45+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/quantify_intrinsic_causal_influence.rst

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic influence on the target node. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data. >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> from dowhy.gcm.uncertainty import estimate_variance >>> np.random.seed(10) # to reproduce these results >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we will model cause-effect relationships as a structural causal model and fit it to the data. >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, data) .. Todo: Use auto module for automatic assignment! Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> gcm.ml.create_linear_regressor(), >>> lambda x, _: estimate_variance(x)) >>> contributions {'X': 33.34300732332951, 'Y': 9.599478688607254, 'Z': 0.9750701113403872} **Interpreting the results:** We estimated the intrinsic influence of ancestors of :math:`Z`, including itself, to its variance. These contributions sum up to the variance of :math:`Z`. We observe that ~76% of the variance of :math:`Z` comes from :math:`X`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Consider the following example to get the intuition behind the notion of "intrinsic" causal influence we seek to measure here. A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the `intrinsic causal influence <https://arxiv.org/pdf/2007.00714.pdf>`_ of a source node to a target node, we need a functional causal model. In particular, we assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. entropy, variance) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> lambda x, _: estimate_variance(x)) .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the uncertainty estimator with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". .. Todo: Add this once confidence intervals is added! Above, we report point estimates of Shapley values from a sample drawn from the estimated joint distribution :math:`\hat{P}_{X, Y, Z}`. To quantify the uncertainty of those point estimates, we now compute their `bootstrap confidence intervals <https://ocw.mit .edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings /MIT18_05S14_Reading24.pdf>`_ by simply running the above a number of times, and aggregating the results. >>> from gcm import confidence_intervals, bootstrap_sampling >>> >>> node_to_mean_contrib, node_to_contrib_conf = confidence_intervals( >>> bootstrap_sampling(gcm.intrinsic_causal_influence, causal_model, 'Z', >>> prediction_model_from_noises_to_target, lambda x, _: estimate_variance(x)), >>> confidence_level=0.95, >>> num_bootstrap_resamples=200) Note that the higher the number of repetitions, the better we are able to approximate the sampling distribution of Shapley values.

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic causal influence on the target node. This method is based on the paper: Dominik Janzing, Patrick Blöbaum, Lenon Minorics, Philipp Faller, Atalanti Mastakouri. `Quantifying intrinsic causal contributions via structure preserving interventions <https://arxiv.org/abs/2007.00714>`_ arXiv:2007.00714, 2021 Let's consider an example from the paper to understand the type of influence being measured here. Imagine a schedule of three trains, ``Train A, Train B`` and ``Train C``, where the departure time of ``Train C`` depends on the arrival time of ``Train B``, and the departure time of ``Train B`` depends on the arrival time of ``Train A``. Suppose ``Train A`` typically experiences much longer delays than ``Train B`` and ``Train C``. The question we want to answer is: How strong is the influence of each train on the delay of ``Train C``? While there are various definitions of influence in the literature, we are interested in the *intrinsic causal influence*, which measures the influence of a node that has not been inherited from its parents, that is, the influence of the noise of a node. The reason for this is that, while ``Train C`` has to wait for ``Train B``, ``Train B`` mostly inherits the delay from ``Train A``. Thus, ``Train A`` should be identified as the node that contributes the most to the delay of ``Train C``. See the :ref:`Understanding the method <understand-method>` section for another example and more details. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data following the example above: >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> X = abs(np.random.normal(loc=0, scale=5, size=1000)) >>> Y = X + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> Z = Y + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Note the larger standard deviation of the 'noise' in :math:`X`. Next, we will model cause-effect relationships as a structural causal model and fit it to the data. Here, we are using the auto module to automatically assign causal mechanisms: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> gcm.auto.assign_causal_mechanisms(causal_model, data) >>> gcm.fit(causal_model, data) Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z') >>> contributions {'X': 8.736841722582117, 'Y': 0.4491606897202768, 'Z': 0.35377942123477574} Note that, although we use a linear relationship here, the method can also handle arbitrary non-linear relationships. **Interpreting the results:** We estimated the intrinsic causal influence of ancestors of :math:`Z`, including itself, to its variance (the default measure). These contributions sum up to the variance of :math:`Z`. As we see here, we observe that ~92% of the variance of :math:`Z` comes from :math:`X`. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Let's look at a different example to explain the intuition behind the notion of "intrinsic" causal influence further: A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the intrinsic causal influence of a source node to a target node, we need a functional causal model. For instance, we can assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. variance or entropy) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=lambda x, _: estimate_variance(x)) Here, we explicitly defined the variance in the parameter ``attribution_func`` as the property we are interested in. .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the ``attribution_func`` with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". **Remark on using the mean for the attribution:** Although the ``attribution_func`` can be customized for a given use case, not all definitions make sense. For instance, using the **mean** does not provide any meaningful results. This is because the way influences are estimated is based on the concept of Shapley values. To understand this better, we can look at a general property of Shapley values, which states that the sum of Shapley values, in our case the sum of the attributions, adds up to :math:`\nu(T) - \nu(\{\})`. Here, :math:`\nu` is a set function (in our case, the expectation of the ``attribution_func``), and :math:`T` is the full set of all players (in our case, all noise variables). Now, if we use the mean, :math:`\nu(T)` becomes :math:`\mathbb{E}_\mathbf{N}[\mathbb{E}[Y | \mathbf{N}]] = \mathbb{E}[Y]`, because the target variable :math:`Y` depends deterministically on all noise variables :math:`\mathbf{N}` in the graphical causal model. Similarly, :math:`\nu(\{\})` becomes :math:`\mathbb{E}[Y | \{\}] = \mathbb{E}[Y]`. This would result in :math:`\mathbb{E}_\mathbb{N}[\mathbb{E}[Y | \mathbb{N}]] - \mathbb{E}[Y | \{\}] = 0`, i.e. the resulting attributions are close to 0. For more details, see Section 3.3 of the paper.

bloebp

a1dcccbc805cb28aa4840fe9bce8338278632a50

12168ea7bd7a30d4c0d6501f69c7161ddb073845

Removed "simple" here. This is more referring to the ``Y = X + N`` setup, since users might think it is restricted to linear relationships.

bloebp

py-why/dowhy

Revise user guide entry for intrinsic causal influence

2023-02-24 21:36:44+00:00

2023-03-07 16:13:45+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/quantify_intrinsic_causal_influence.rst

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic influence on the target node. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data. >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> from dowhy.gcm.uncertainty import estimate_variance >>> np.random.seed(10) # to reproduce these results >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we will model cause-effect relationships as a structural causal model and fit it to the data. >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, data) .. Todo: Use auto module for automatic assignment! Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> gcm.ml.create_linear_regressor(), >>> lambda x, _: estimate_variance(x)) >>> contributions {'X': 33.34300732332951, 'Y': 9.599478688607254, 'Z': 0.9750701113403872} **Interpreting the results:** We estimated the intrinsic influence of ancestors of :math:`Z`, including itself, to its variance. These contributions sum up to the variance of :math:`Z`. We observe that ~76% of the variance of :math:`Z` comes from :math:`X`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Consider the following example to get the intuition behind the notion of "intrinsic" causal influence we seek to measure here. A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the `intrinsic causal influence <https://arxiv.org/pdf/2007.00714.pdf>`_ of a source node to a target node, we need a functional causal model. In particular, we assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. entropy, variance) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> lambda x, _: estimate_variance(x)) .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the uncertainty estimator with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". .. Todo: Add this once confidence intervals is added! Above, we report point estimates of Shapley values from a sample drawn from the estimated joint distribution :math:`\hat{P}_{X, Y, Z}`. To quantify the uncertainty of those point estimates, we now compute their `bootstrap confidence intervals <https://ocw.mit .edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings /MIT18_05S14_Reading24.pdf>`_ by simply running the above a number of times, and aggregating the results. >>> from gcm import confidence_intervals, bootstrap_sampling >>> >>> node_to_mean_contrib, node_to_contrib_conf = confidence_intervals( >>> bootstrap_sampling(gcm.intrinsic_causal_influence, causal_model, 'Z', >>> prediction_model_from_noises_to_target, lambda x, _: estimate_variance(x)), >>> confidence_level=0.95, >>> num_bootstrap_resamples=200) Note that the higher the number of repetitions, the better we are able to approximate the sampling distribution of Shapley values.

Quantifying Intrinsic Causal Influence ====================================== By quantifying intrinsic causal influence, we answer the question: How strong is the causal influence of a source node to a target node that is not inherited from the parents of the source node? Naturally, descendants will have a zero intrinsic causal influence on the target node. This method is based on the paper: Dominik Janzing, Patrick Blöbaum, Lenon Minorics, Philipp Faller, Atalanti Mastakouri. `Quantifying intrinsic causal contributions via structure preserving interventions <https://arxiv.org/abs/2007.00714>`_ arXiv:2007.00714, 2021 Let's consider an example from the paper to understand the type of influence being measured here. Imagine a schedule of three trains, ``Train A, Train B`` and ``Train C``, where the departure time of ``Train C`` depends on the arrival time of ``Train B``, and the departure time of ``Train B`` depends on the arrival time of ``Train A``. Suppose ``Train A`` typically experiences much longer delays than ``Train B`` and ``Train C``. The question we want to answer is: How strong is the influence of each train on the delay of ``Train C``? While there are various definitions of influence in the literature, we are interested in the *intrinsic causal influence*, which measures the influence of a node that has not been inherited from its parents, that is, the influence of the noise of a node. The reason for this is that, while ``Train C`` has to wait for ``Train B``, ``Train B`` mostly inherits the delay from ``Train A``. Thus, ``Train A`` should be identified as the node that contributes the most to the delay of ``Train C``. See the :ref:`Understanding the method <understand-method>` section for another example and more details. How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data following the example above: >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> X = abs(np.random.normal(loc=0, scale=5, size=1000)) >>> Y = X + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> Z = Y + abs(np.random.normal(loc=0, scale=1, size=1000)) >>> data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Note the larger standard deviation of the 'noise' in :math:`X`. Next, we will model cause-effect relationships as a structural causal model and fit it to the data. Here, we are using the auto module to automatically assign causal mechanisms: >>> causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> gcm.auto.assign_causal_mechanisms(causal_model, data) >>> gcm.fit(causal_model, data) Finally, we can ask for the intrinsic causal influences of ancestors to a node of interest (e.g., :math:`Z`). >>> contributions = gcm.intrinsic_causal_influence(causal_model, 'Z') >>> contributions {'X': 8.736841722582117, 'Y': 0.4491606897202768, 'Z': 0.35377942123477574} Note that, although we use a linear relationship here, the method can also handle arbitrary non-linear relationships. **Interpreting the results:** We estimated the intrinsic causal influence of ancestors of :math:`Z`, including itself, to its variance (the default measure). These contributions sum up to the variance of :math:`Z`. As we see here, we observe that ~92% of the variance of :math:`Z` comes from :math:`X`. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^^ Let's look at a different example to explain the intuition behind the notion of "intrinsic" causal influence further: A charity event is organised to collect funds to help an orphanage. At the end of the event, a donation box is passed around to each participant. Since the donation is voluntary, some may not donate for various reasons. For instance, they may not have the cash. In this scenario, a participant that simply passes the donation box to the other participant does not contribute anything to the collective donation after all. Each person's contribution then is simply the amount they donated. To measure the intrinsic causal influence of a source node to a target node, we need a functional causal model. For instance, we can assume that the causal model of each node follows an additive noise model (ANM), i.e. :math:`X_j := f_j (\textrm{PA}_j) + N_j`, where :math:`\textrm{PA}_j` are the parents of node :math:`X_j` in the causal graph, and :math:`N_j` is the independent unobserved noise term. To compute the "intrinsic" contribution of ancestors of :math:`X_n` to some property (e.g. variance or entropy) of the marginal distribution of :math:`X_n`, we first have to set up our causal graph, and learn the causal model of each node from the dataset. Consider a causal graph :math:`X \rightarrow Y \rightarrow Z` as in the code example above, induced by the following ANMs. .. math:: X &:= N_X\\ Y &:= 2 X + N_Y\\ Z &:= 3 Y + N_Z \;, where :math:`N_w \sim \mathcal{N}(0, 1)`, for all :math:`w \in \{X, Y, Z\}`, are standard Normal noise variables. Suppose that we are interested in the contribution of each variable to the *variance* of the target :math:`Z`, i.e. :math:`\mathrm{Var}[Z]`. If there were no noise variables, everything can be contributed to the root node :math:`X` as all other variables would then be its deterministic function. The intrinsic contribution of each variable to the target quantity :math:`\mathrm{Var}[Z]` is then really the contribution of corresponding noise term. To compute "intrinsic" contribution, we also require conditional distributions of :math:`Z` given subsets of noise variables :math:`N_T`, i.e., :math:`P_{Z \mid N_T}`, where :math:`T \subseteq \{X, Y, Z\}`. We estimate them using an ANM. To this end, we have to specify the prediction model from a subset of noise variables to the target. Below, we quantify the intrinsic causal influence of :math:`X, Y` and :math:`Z` to :math:`\mathrm{Var}[Z]` using a linear prediction model from noise variables to :math:`Z`. >>> from dowhy.gcm.uncertainty import estimate_variance >>> prediction_model_from_noises_to_target = gcm.ml.create_linear_regressor() >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=lambda x, _: estimate_variance(x)) Here, we explicitly defined the variance in the parameter ``attribution_func`` as the property we are interested in. .. note:: While using variance as uncertainty estimator gives valuable information about the contribution of nodes to the squared deviations in the target, one might be rather interested in other quantities, such as absolute deviations. This can also be simply computed by replacing the ``attribution_func`` with a custom function: >>> mean_absolute_deviation_estimator = lambda x: np.mean(abs(x)) >>> node_to_contribution = gcm.intrinsic_causal_influence(causal_model, 'Z', >>> prediction_model_from_noises_to_target, >>> attribution_func=mean_absolute_deviation_estimator) If the choice of a prediction model is unclear, the prediction model parameter can also be set to "auto". **Remark on using the mean for the attribution:** Although the ``attribution_func`` can be customized for a given use case, not all definitions make sense. For instance, using the **mean** does not provide any meaningful results. This is because the way influences are estimated is based on the concept of Shapley values. To understand this better, we can look at a general property of Shapley values, which states that the sum of Shapley values, in our case the sum of the attributions, adds up to :math:`\nu(T) - \nu(\{\})`. Here, :math:`\nu` is a set function (in our case, the expectation of the ``attribution_func``), and :math:`T` is the full set of all players (in our case, all noise variables). Now, if we use the mean, :math:`\nu(T)` becomes :math:`\mathbb{E}_\mathbf{N}[\mathbb{E}[Y | \mathbf{N}]] = \mathbb{E}[Y]`, because the target variable :math:`Y` depends deterministically on all noise variables :math:`\mathbf{N}` in the graphical causal model. Similarly, :math:`\nu(\{\})` becomes :math:`\mathbb{E}[Y | \{\}] = \mathbb{E}[Y]`. This would result in :math:`\mathbb{E}_\mathbb{N}[\mathbb{E}[Y | \mathbb{N}]] - \mathbb{E}[Y | \{\}] = 0`, i.e. the resulting attributions are close to 0. For more details, see Section 3.3 of the paper.

bloebp

a1dcccbc805cb28aa4840fe9bce8338278632a50

12168ea7bd7a30d4c0d6501f69c7161ddb073845

Fixed

bloebp

py-why/dowhy

Revise attributing distributional changes user guide entry

2023-02-17 22:20:40+00:00

2023-03-07 16:14:00+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/attribute_distributional_changes.rst

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: What mechanism in my system changed between two sets of data? For example, in a distributed computing system, we want to know why an important system metric changed in a negative way. How to use it ^^^^^^^^^^^^^^ To see how the method works, let's take the example from above and assume we have a system of three services X, Y, Z, producing latency numbers. The first dataset ``data_old`` is before the deployment, ``data_new`` is after the deployment: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=1, size=1000) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=1, size=1000) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) The change here simulates an accidental conversion of multi-threaded code into sequential one (waiting for X and Y in parallel vs. waiting for them sequentially). Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z')])) # X -> Z <- Y >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Finally, we attribute changes in distributions to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'Z') >>> attributions {'X': -0.0066425020480165905, 'Y': 0.009816959724738061, 'Z': 0.21957816956354193} As we can see, :math:`Z` got the highest attribution score here, which matches what we would expect, given that we changed the mechanism for variable :math:`Z` in our data generation. As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset.

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: **What mechanism in my system changed between two sets of data? Or in other words, which node in my data behaves differently?** Here we want to identify the node or nodes in the graph where the causal mechanism has changed. For example, if we detect an uptick in latency of our application within a microservice architecture, we aim to identify the node/component whose behavior has altered. has changed. DoWhy implements a method to identify and attribute changes in a distribution to changes in causal mechanisms of upstream nodes following the paper: Kailash Budhathoki, Dominik Janzing, Patrick Blöbaum, Hoiyi Ng. `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_ Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1666-1674, 2021. How to use it ^^^^^^^^^^^^^^ To see how to use the method, let's take the microservice example from above and assume we have a system of four services :math:`X, Y, Z, W`, each of which monitors latencies. Suppose we plan to carry out a new deployment and record the latencies before and after the deployment. We will refer to the latency data gathered prior to the deployment as ``data_old`` and the data gathered after the deployment as ``data_new``: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) Here, we change the behaviour of :math:`Z`, which simulates an accidental conversion of multi-threaded code into sequential one (waiting for :math:`X` and :math:`Y` in parallel vs. waiting for them sequentially). This will change the distribution of :math:`Z` and subsequently :math:`W`. Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z'), ('Z', 'W')])) # (X, Y) -> Z -> W >>> gcm.auto.assign_causal_mechanisms(causal_model, data_old) Finally, we attribute changes in distributions of :math:`W` to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'W') >>> attributions {'W': 0.012553173521649849, 'X': -0.007493424287710609, 'Y': 0.0013256550695736396, 'Z': 0.7396701922473544} Although the distribution of :math:`W` has changed as well, the method attributes the change almost completely to :math:`Z` with negligible scores for the other variables. This is in line with our expectations since we only altered the mechanism of :math:`Z`. Note that the unit of the scores depends on the used measure (see the next section). As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ The idea behind this method is to *systematically* replace the causal mechanism learned based on the old dataset with the mechanism learned based on the new dataset. After each replacement, new samples are generated for the target node, where the data generation process is a mixture of old and new mechanisms. Our goal is to identify the mechanisms that have changed, which would lead to a different marginal distribution of the target, while unchanged mechanisms would result in the same marginal distribution. To achieve this, we employ the idea of a Shapley symmetrization to systematically replace the mechanisms. This enables us to identify which nodes have changed and to estimate an attribution score with respect to some measure. Note that a change in the mechanism could be due to a functional change in the underlying model or a change in the (unobserved) noise distribution. However, both changes would lead to a change in the mechanism. The steps here are as follows: .. image:: dist_change.png 1. Estimate the conditional distributions from 'old' data (e.g., latencies before deployment): :math:`P_{X_1, ..., X_n} = \prod_j P_{X_j | PA_j}`, where :math:`P_{X_j | PA_j}` is the causal mechanism of node :math:`X_j` and :math:`PA_j` the parents of node :math:`X_j` 2. Estimate the conditional distributions from 'new' data (e.g., latencies after deployment): :math:`\tilde P_{X_1, ..., X_n} = \prod_j \tilde P_{X_j | PA_j}` 3. Replace mechanisms based on the 'old' data with mechanisms based on the 'new' data systematically, one by one. For this, replace :math:`P_{X_j | PA_j}` by :math:`\tilde P_{X_j | PA_j}` for each :math:`j`. If nodes in :math:`T \subseteq \{1, ..., n\}` have been replaced before, we get :math:`\tilde P^{X_n}_T = \sum_{x_1, ..., x_{n-1}} \prod_{j \in T} \tilde P_{X_j | PA_j} \prod_{j \notin T} P_{X_j | PA_j}`, a new marginal for node :math:`n`. 4. Attribute the change in the marginal given :math:`T` to :math:`X_j` using Shapley values by comparing :math:`P^{X_n}_{T \bigcup \{j\}}` and :math:`P^{X_n}_{T}`. Here, we can use different measures to capture the change, such as KL divergence to the original distribution or difference in variances etc. For more detailed explanation, see the corresponding paper: `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_

bloebp

12168ea7bd7a30d4c0d6501f69c7161ddb073845

5d449be765fbb04d77a35d2ace7978bfc6d90309

Is this really better? Note that we already use the word "mechanism" in our methods and language. So I believe it does make sense to refer to it here, no?

petergtz

py-why/dowhy

Revise attributing distributional changes user guide entry

2023-02-17 22:20:40+00:00

2023-03-07 16:14:00+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/attribute_distributional_changes.rst

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: What mechanism in my system changed between two sets of data? For example, in a distributed computing system, we want to know why an important system metric changed in a negative way. How to use it ^^^^^^^^^^^^^^ To see how the method works, let's take the example from above and assume we have a system of three services X, Y, Z, producing latency numbers. The first dataset ``data_old`` is before the deployment, ``data_new`` is after the deployment: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=1, size=1000) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=1, size=1000) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) The change here simulates an accidental conversion of multi-threaded code into sequential one (waiting for X and Y in parallel vs. waiting for them sequentially). Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z')])) # X -> Z <- Y >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Finally, we attribute changes in distributions to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'Z') >>> attributions {'X': -0.0066425020480165905, 'Y': 0.009816959724738061, 'Z': 0.21957816956354193} As we can see, :math:`Z` got the highest attribution score here, which matches what we would expect, given that we changed the mechanism for variable :math:`Z` in our data generation. As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset.

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: **What mechanism in my system changed between two sets of data? Or in other words, which node in my data behaves differently?** Here we want to identify the node or nodes in the graph where the causal mechanism has changed. For example, if we detect an uptick in latency of our application within a microservice architecture, we aim to identify the node/component whose behavior has altered. has changed. DoWhy implements a method to identify and attribute changes in a distribution to changes in causal mechanisms of upstream nodes following the paper: Kailash Budhathoki, Dominik Janzing, Patrick Blöbaum, Hoiyi Ng. `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_ Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1666-1674, 2021. How to use it ^^^^^^^^^^^^^^ To see how to use the method, let's take the microservice example from above and assume we have a system of four services :math:`X, Y, Z, W`, each of which monitors latencies. Suppose we plan to carry out a new deployment and record the latencies before and after the deployment. We will refer to the latency data gathered prior to the deployment as ``data_old`` and the data gathered after the deployment as ``data_new``: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) Here, we change the behaviour of :math:`Z`, which simulates an accidental conversion of multi-threaded code into sequential one (waiting for :math:`X` and :math:`Y` in parallel vs. waiting for them sequentially). This will change the distribution of :math:`Z` and subsequently :math:`W`. Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z'), ('Z', 'W')])) # (X, Y) -> Z -> W >>> gcm.auto.assign_causal_mechanisms(causal_model, data_old) Finally, we attribute changes in distributions of :math:`W` to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'W') >>> attributions {'W': 0.012553173521649849, 'X': -0.007493424287710609, 'Y': 0.0013256550695736396, 'Z': 0.7396701922473544} Although the distribution of :math:`W` has changed as well, the method attributes the change almost completely to :math:`Z` with negligible scores for the other variables. This is in line with our expectations since we only altered the mechanism of :math:`Z`. Note that the unit of the scores depends on the used measure (see the next section). As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ The idea behind this method is to *systematically* replace the causal mechanism learned based on the old dataset with the mechanism learned based on the new dataset. After each replacement, new samples are generated for the target node, where the data generation process is a mixture of old and new mechanisms. Our goal is to identify the mechanisms that have changed, which would lead to a different marginal distribution of the target, while unchanged mechanisms would result in the same marginal distribution. To achieve this, we employ the idea of a Shapley symmetrization to systematically replace the mechanisms. This enables us to identify which nodes have changed and to estimate an attribution score with respect to some measure. Note that a change in the mechanism could be due to a functional change in the underlying model or a change in the (unobserved) noise distribution. However, both changes would lead to a change in the mechanism. The steps here are as follows: .. image:: dist_change.png 1. Estimate the conditional distributions from 'old' data (e.g., latencies before deployment): :math:`P_{X_1, ..., X_n} = \prod_j P_{X_j | PA_j}`, where :math:`P_{X_j | PA_j}` is the causal mechanism of node :math:`X_j` and :math:`PA_j` the parents of node :math:`X_j` 2. Estimate the conditional distributions from 'new' data (e.g., latencies after deployment): :math:`\tilde P_{X_1, ..., X_n} = \prod_j \tilde P_{X_j | PA_j}` 3. Replace mechanisms based on the 'old' data with mechanisms based on the 'new' data systematically, one by one. For this, replace :math:`P_{X_j | PA_j}` by :math:`\tilde P_{X_j | PA_j}` for each :math:`j`. If nodes in :math:`T \subseteq \{1, ..., n\}` have been replaced before, we get :math:`\tilde P^{X_n}_T = \sum_{x_1, ..., x_{n-1}} \prod_{j \in T} \tilde P_{X_j | PA_j} \prod_{j \notin T} P_{X_j | PA_j}`, a new marginal for node :math:`n`. 4. Attribute the change in the marginal given :math:`T` to :math:`X_j` using Shapley values by comparing :math:`P^{X_n}_{T \bigcup \{j\}}` and :math:`P^{X_n}_{T}`. Here, we can use different measures to capture the change, such as KL divergence to the original distribution or difference in variances etc. For more detailed explanation, see the corresponding paper: `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_

bloebp

12168ea7bd7a30d4c0d6501f69c7161ddb073845

5d449be765fbb04d77a35d2ace7978bfc6d90309

It would definitely make sense, but seeing it from a perspective of someone who just wants to "quickly" look through the functionalities, I think this formulation helps more in understanding what the purpose of the method is. Otherwise, one first needs to understand what we mean by a 'mechanism' etc.

bloebp

py-why/dowhy

Revise attributing distributional changes user guide entry

2023-02-17 22:20:40+00:00

2023-03-07 16:14:00+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/attribute_distributional_changes.rst

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: What mechanism in my system changed between two sets of data? For example, in a distributed computing system, we want to know why an important system metric changed in a negative way. How to use it ^^^^^^^^^^^^^^ To see how the method works, let's take the example from above and assume we have a system of three services X, Y, Z, producing latency numbers. The first dataset ``data_old`` is before the deployment, ``data_new`` is after the deployment: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=1, size=1000) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=1, size=1000) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) The change here simulates an accidental conversion of multi-threaded code into sequential one (waiting for X and Y in parallel vs. waiting for them sequentially). Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z')])) # X -> Z <- Y >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Finally, we attribute changes in distributions to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'Z') >>> attributions {'X': -0.0066425020480165905, 'Y': 0.009816959724738061, 'Z': 0.21957816956354193} As we can see, :math:`Z` got the highest attribution score here, which matches what we would expect, given that we changed the mechanism for variable :math:`Z` in our data generation. As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset.

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: **What mechanism in my system changed between two sets of data? Or in other words, which node in my data behaves differently?** Here we want to identify the node or nodes in the graph where the causal mechanism has changed. For example, if we detect an uptick in latency of our application within a microservice architecture, we aim to identify the node/component whose behavior has altered. has changed. DoWhy implements a method to identify and attribute changes in a distribution to changes in causal mechanisms of upstream nodes following the paper: Kailash Budhathoki, Dominik Janzing, Patrick Blöbaum, Hoiyi Ng. `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_ Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1666-1674, 2021. How to use it ^^^^^^^^^^^^^^ To see how to use the method, let's take the microservice example from above and assume we have a system of four services :math:`X, Y, Z, W`, each of which monitors latencies. Suppose we plan to carry out a new deployment and record the latencies before and after the deployment. We will refer to the latency data gathered prior to the deployment as ``data_old`` and the data gathered after the deployment as ``data_new``: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) Here, we change the behaviour of :math:`Z`, which simulates an accidental conversion of multi-threaded code into sequential one (waiting for :math:`X` and :math:`Y` in parallel vs. waiting for them sequentially). This will change the distribution of :math:`Z` and subsequently :math:`W`. Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z'), ('Z', 'W')])) # (X, Y) -> Z -> W >>> gcm.auto.assign_causal_mechanisms(causal_model, data_old) Finally, we attribute changes in distributions of :math:`W` to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'W') >>> attributions {'W': 0.012553173521649849, 'X': -0.007493424287710609, 'Y': 0.0013256550695736396, 'Z': 0.7396701922473544} Although the distribution of :math:`W` has changed as well, the method attributes the change almost completely to :math:`Z` with negligible scores for the other variables. This is in line with our expectations since we only altered the mechanism of :math:`Z`. Note that the unit of the scores depends on the used measure (see the next section). As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ The idea behind this method is to *systematically* replace the causal mechanism learned based on the old dataset with the mechanism learned based on the new dataset. After each replacement, new samples are generated for the target node, where the data generation process is a mixture of old and new mechanisms. Our goal is to identify the mechanisms that have changed, which would lead to a different marginal distribution of the target, while unchanged mechanisms would result in the same marginal distribution. To achieve this, we employ the idea of a Shapley symmetrization to systematically replace the mechanisms. This enables us to identify which nodes have changed and to estimate an attribution score with respect to some measure. Note that a change in the mechanism could be due to a functional change in the underlying model or a change in the (unobserved) noise distribution. However, both changes would lead to a change in the mechanism. The steps here are as follows: .. image:: dist_change.png 1. Estimate the conditional distributions from 'old' data (e.g., latencies before deployment): :math:`P_{X_1, ..., X_n} = \prod_j P_{X_j | PA_j}`, where :math:`P_{X_j | PA_j}` is the causal mechanism of node :math:`X_j` and :math:`PA_j` the parents of node :math:`X_j` 2. Estimate the conditional distributions from 'new' data (e.g., latencies after deployment): :math:`\tilde P_{X_1, ..., X_n} = \prod_j \tilde P_{X_j | PA_j}` 3. Replace mechanisms based on the 'old' data with mechanisms based on the 'new' data systematically, one by one. For this, replace :math:`P_{X_j | PA_j}` by :math:`\tilde P_{X_j | PA_j}` for each :math:`j`. If nodes in :math:`T \subseteq \{1, ..., n\}` have been replaced before, we get :math:`\tilde P^{X_n}_T = \sum_{x_1, ..., x_{n-1}} \prod_{j \in T} \tilde P_{X_j | PA_j} \prod_{j \notin T} P_{X_j | PA_j}`, a new marginal for node :math:`n`. 4. Attribute the change in the marginal given :math:`T` to :math:`X_j` using Shapley values by comparing :math:`P^{X_n}_{T \bigcup \{j\}}` and :math:`P^{X_n}_{T}`. Here, we can use different measures to capture the change, such as KL divergence to the original distribution or difference in variances etc. For more detailed explanation, see the corresponding paper: `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_

bloebp

12168ea7bd7a30d4c0d6501f69c7161ddb073845

5d449be765fbb04d77a35d2ace7978bfc6d90309

Can we have both? One for continuity across the documentation and one for the quick reader? "What mechanism ....? Or in other words, which node in my data behaves differently?"

emrekiciman

py-why/dowhy

Revise attributing distributional changes user guide entry

2023-02-17 22:20:40+00:00

2023-03-07 16:14:00+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/attribute_distributional_changes.rst

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: What mechanism in my system changed between two sets of data? For example, in a distributed computing system, we want to know why an important system metric changed in a negative way. How to use it ^^^^^^^^^^^^^^ To see how the method works, let's take the example from above and assume we have a system of three services X, Y, Z, producing latency numbers. The first dataset ``data_old`` is before the deployment, ``data_new`` is after the deployment: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=1, size=1000) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=1, size=1000) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) The change here simulates an accidental conversion of multi-threaded code into sequential one (waiting for X and Y in parallel vs. waiting for them sequentially). Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z')])) # X -> Z <- Y >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Finally, we attribute changes in distributions to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'Z') >>> attributions {'X': -0.0066425020480165905, 'Y': 0.009816959724738061, 'Z': 0.21957816956354193} As we can see, :math:`Z` got the highest attribution score here, which matches what we would expect, given that we changed the mechanism for variable :math:`Z` in our data generation. As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset.

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: **What mechanism in my system changed between two sets of data? Or in other words, which node in my data behaves differently?** Here we want to identify the node or nodes in the graph where the causal mechanism has changed. For example, if we detect an uptick in latency of our application within a microservice architecture, we aim to identify the node/component whose behavior has altered. has changed. DoWhy implements a method to identify and attribute changes in a distribution to changes in causal mechanisms of upstream nodes following the paper: Kailash Budhathoki, Dominik Janzing, Patrick Blöbaum, Hoiyi Ng. `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_ Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1666-1674, 2021. How to use it ^^^^^^^^^^^^^^ To see how to use the method, let's take the microservice example from above and assume we have a system of four services :math:`X, Y, Z, W`, each of which monitors latencies. Suppose we plan to carry out a new deployment and record the latencies before and after the deployment. We will refer to the latency data gathered prior to the deployment as ``data_old`` and the data gathered after the deployment as ``data_new``: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) Here, we change the behaviour of :math:`Z`, which simulates an accidental conversion of multi-threaded code into sequential one (waiting for :math:`X` and :math:`Y` in parallel vs. waiting for them sequentially). This will change the distribution of :math:`Z` and subsequently :math:`W`. Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z'), ('Z', 'W')])) # (X, Y) -> Z -> W >>> gcm.auto.assign_causal_mechanisms(causal_model, data_old) Finally, we attribute changes in distributions of :math:`W` to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'W') >>> attributions {'W': 0.012553173521649849, 'X': -0.007493424287710609, 'Y': 0.0013256550695736396, 'Z': 0.7396701922473544} Although the distribution of :math:`W` has changed as well, the method attributes the change almost completely to :math:`Z` with negligible scores for the other variables. This is in line with our expectations since we only altered the mechanism of :math:`Z`. Note that the unit of the scores depends on the used measure (see the next section). As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ The idea behind this method is to *systematically* replace the causal mechanism learned based on the old dataset with the mechanism learned based on the new dataset. After each replacement, new samples are generated for the target node, where the data generation process is a mixture of old and new mechanisms. Our goal is to identify the mechanisms that have changed, which would lead to a different marginal distribution of the target, while unchanged mechanisms would result in the same marginal distribution. To achieve this, we employ the idea of a Shapley symmetrization to systematically replace the mechanisms. This enables us to identify which nodes have changed and to estimate an attribution score with respect to some measure. Note that a change in the mechanism could be due to a functional change in the underlying model or a change in the (unobserved) noise distribution. However, both changes would lead to a change in the mechanism. The steps here are as follows: .. image:: dist_change.png 1. Estimate the conditional distributions from 'old' data (e.g., latencies before deployment): :math:`P_{X_1, ..., X_n} = \prod_j P_{X_j | PA_j}`, where :math:`P_{X_j | PA_j}` is the causal mechanism of node :math:`X_j` and :math:`PA_j` the parents of node :math:`X_j` 2. Estimate the conditional distributions from 'new' data (e.g., latencies after deployment): :math:`\tilde P_{X_1, ..., X_n} = \prod_j \tilde P_{X_j | PA_j}` 3. Replace mechanisms based on the 'old' data with mechanisms based on the 'new' data systematically, one by one. For this, replace :math:`P_{X_j | PA_j}` by :math:`\tilde P_{X_j | PA_j}` for each :math:`j`. If nodes in :math:`T \subseteq \{1, ..., n\}` have been replaced before, we get :math:`\tilde P^{X_n}_T = \sum_{x_1, ..., x_{n-1}} \prod_{j \in T} \tilde P_{X_j | PA_j} \prod_{j \notin T} P_{X_j | PA_j}`, a new marginal for node :math:`n`. 4. Attribute the change in the marginal given :math:`T` to :math:`X_j` using Shapley values by comparing :math:`P^{X_n}_{T \bigcup \{j\}}` and :math:`P^{X_n}_{T}`. Here, we can use different measures to capture the change, such as KL divergence to the original distribution or difference in variances etc. For more detailed explanation, see the corresponding paper: `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_

bloebp

12168ea7bd7a30d4c0d6501f69c7161ddb073845

5d449be765fbb04d77a35d2ace7978bfc6d90309

That's a good compromise, will change it.

bloebp

py-why/dowhy

Revise attributing distributional changes user guide entry

2023-02-17 22:20:40+00:00

2023-03-07 16:14:00+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/attribute_distributional_changes.rst

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: What mechanism in my system changed between two sets of data? For example, in a distributed computing system, we want to know why an important system metric changed in a negative way. How to use it ^^^^^^^^^^^^^^ To see how the method works, let's take the example from above and assume we have a system of three services X, Y, Z, producing latency numbers. The first dataset ``data_old`` is before the deployment, ``data_new`` is after the deployment: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=1, size=1000) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=1, size=1000) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) The change here simulates an accidental conversion of multi-threaded code into sequential one (waiting for X and Y in parallel vs. waiting for them sequentially). Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z')])) # X -> Z <- Y >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Finally, we attribute changes in distributions to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'Z') >>> attributions {'X': -0.0066425020480165905, 'Y': 0.009816959724738061, 'Z': 0.21957816956354193} As we can see, :math:`Z` got the highest attribution score here, which matches what we would expect, given that we changed the mechanism for variable :math:`Z` in our data generation. As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset.

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: **What mechanism in my system changed between two sets of data? Or in other words, which node in my data behaves differently?** Here we want to identify the node or nodes in the graph where the causal mechanism has changed. For example, if we detect an uptick in latency of our application within a microservice architecture, we aim to identify the node/component whose behavior has altered. has changed. DoWhy implements a method to identify and attribute changes in a distribution to changes in causal mechanisms of upstream nodes following the paper: Kailash Budhathoki, Dominik Janzing, Patrick Blöbaum, Hoiyi Ng. `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_ Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1666-1674, 2021. How to use it ^^^^^^^^^^^^^^ To see how to use the method, let's take the microservice example from above and assume we have a system of four services :math:`X, Y, Z, W`, each of which monitors latencies. Suppose we plan to carry out a new deployment and record the latencies before and after the deployment. We will refer to the latency data gathered prior to the deployment as ``data_old`` and the data gathered after the deployment as ``data_new``: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) Here, we change the behaviour of :math:`Z`, which simulates an accidental conversion of multi-threaded code into sequential one (waiting for :math:`X` and :math:`Y` in parallel vs. waiting for them sequentially). This will change the distribution of :math:`Z` and subsequently :math:`W`. Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z'), ('Z', 'W')])) # (X, Y) -> Z -> W >>> gcm.auto.assign_causal_mechanisms(causal_model, data_old) Finally, we attribute changes in distributions of :math:`W` to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'W') >>> attributions {'W': 0.012553173521649849, 'X': -0.007493424287710609, 'Y': 0.0013256550695736396, 'Z': 0.7396701922473544} Although the distribution of :math:`W` has changed as well, the method attributes the change almost completely to :math:`Z` with negligible scores for the other variables. This is in line with our expectations since we only altered the mechanism of :math:`Z`. Note that the unit of the scores depends on the used measure (see the next section). As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ The idea behind this method is to *systematically* replace the causal mechanism learned based on the old dataset with the mechanism learned based on the new dataset. After each replacement, new samples are generated for the target node, where the data generation process is a mixture of old and new mechanisms. Our goal is to identify the mechanisms that have changed, which would lead to a different marginal distribution of the target, while unchanged mechanisms would result in the same marginal distribution. To achieve this, we employ the idea of a Shapley symmetrization to systematically replace the mechanisms. This enables us to identify which nodes have changed and to estimate an attribution score with respect to some measure. Note that a change in the mechanism could be due to a functional change in the underlying model or a change in the (unobserved) noise distribution. However, both changes would lead to a change in the mechanism. The steps here are as follows: .. image:: dist_change.png 1. Estimate the conditional distributions from 'old' data (e.g., latencies before deployment): :math:`P_{X_1, ..., X_n} = \prod_j P_{X_j | PA_j}`, where :math:`P_{X_j | PA_j}` is the causal mechanism of node :math:`X_j` and :math:`PA_j` the parents of node :math:`X_j` 2. Estimate the conditional distributions from 'new' data (e.g., latencies after deployment): :math:`\tilde P_{X_1, ..., X_n} = \prod_j \tilde P_{X_j | PA_j}` 3. Replace mechanisms based on the 'old' data with mechanisms based on the 'new' data systematically, one by one. For this, replace :math:`P_{X_j | PA_j}` by :math:`\tilde P_{X_j | PA_j}` for each :math:`j`. If nodes in :math:`T \subseteq \{1, ..., n\}` have been replaced before, we get :math:`\tilde P^{X_n}_T = \sum_{x_1, ..., x_{n-1}} \prod_{j \in T} \tilde P_{X_j | PA_j} \prod_{j \notin T} P_{X_j | PA_j}`, a new marginal for node :math:`n`. 4. Attribute the change in the marginal given :math:`T` to :math:`X_j` using Shapley values by comparing :math:`P^{X_n}_{T \bigcup \{j\}}` and :math:`P^{X_n}_{T}`. Here, we can use different measures to capture the change, such as KL divergence to the original distribution or difference in variances etc. For more detailed explanation, see the corresponding paper: `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_

bloebp

12168ea7bd7a30d4c0d6501f69c7161ddb073845

5d449be765fbb04d77a35d2ace7978bfc6d90309

uptick in latency of ___? application?

kailashbuki

py-why/dowhy

Revise attributing distributional changes user guide entry

2023-02-17 22:20:40+00:00

2023-03-07 16:14:00+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/attribute_distributional_changes.rst

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: What mechanism in my system changed between two sets of data? For example, in a distributed computing system, we want to know why an important system metric changed in a negative way. How to use it ^^^^^^^^^^^^^^ To see how the method works, let's take the example from above and assume we have a system of three services X, Y, Z, producing latency numbers. The first dataset ``data_old`` is before the deployment, ``data_new`` is after the deployment: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=1, size=1000) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=1, size=1000) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) The change here simulates an accidental conversion of multi-threaded code into sequential one (waiting for X and Y in parallel vs. waiting for them sequentially). Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z')])) # X -> Z <- Y >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Finally, we attribute changes in distributions to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'Z') >>> attributions {'X': -0.0066425020480165905, 'Y': 0.009816959724738061, 'Z': 0.21957816956354193} As we can see, :math:`Z` got the highest attribution score here, which matches what we would expect, given that we changed the mechanism for variable :math:`Z` in our data generation. As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset.

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: **What mechanism in my system changed between two sets of data? Or in other words, which node in my data behaves differently?** Here we want to identify the node or nodes in the graph where the causal mechanism has changed. For example, if we detect an uptick in latency of our application within a microservice architecture, we aim to identify the node/component whose behavior has altered. has changed. DoWhy implements a method to identify and attribute changes in a distribution to changes in causal mechanisms of upstream nodes following the paper: Kailash Budhathoki, Dominik Janzing, Patrick Blöbaum, Hoiyi Ng. `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_ Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1666-1674, 2021. How to use it ^^^^^^^^^^^^^^ To see how to use the method, let's take the microservice example from above and assume we have a system of four services :math:`X, Y, Z, W`, each of which monitors latencies. Suppose we plan to carry out a new deployment and record the latencies before and after the deployment. We will refer to the latency data gathered prior to the deployment as ``data_old`` and the data gathered after the deployment as ``data_new``: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) Here, we change the behaviour of :math:`Z`, which simulates an accidental conversion of multi-threaded code into sequential one (waiting for :math:`X` and :math:`Y` in parallel vs. waiting for them sequentially). This will change the distribution of :math:`Z` and subsequently :math:`W`. Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z'), ('Z', 'W')])) # (X, Y) -> Z -> W >>> gcm.auto.assign_causal_mechanisms(causal_model, data_old) Finally, we attribute changes in distributions of :math:`W` to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'W') >>> attributions {'W': 0.012553173521649849, 'X': -0.007493424287710609, 'Y': 0.0013256550695736396, 'Z': 0.7396701922473544} Although the distribution of :math:`W` has changed as well, the method attributes the change almost completely to :math:`Z` with negligible scores for the other variables. This is in line with our expectations since we only altered the mechanism of :math:`Z`. Note that the unit of the scores depends on the used measure (see the next section). As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ The idea behind this method is to *systematically* replace the causal mechanism learned based on the old dataset with the mechanism learned based on the new dataset. After each replacement, new samples are generated for the target node, where the data generation process is a mixture of old and new mechanisms. Our goal is to identify the mechanisms that have changed, which would lead to a different marginal distribution of the target, while unchanged mechanisms would result in the same marginal distribution. To achieve this, we employ the idea of a Shapley symmetrization to systematically replace the mechanisms. This enables us to identify which nodes have changed and to estimate an attribution score with respect to some measure. Note that a change in the mechanism could be due to a functional change in the underlying model or a change in the (unobserved) noise distribution. However, both changes would lead to a change in the mechanism. The steps here are as follows: .. image:: dist_change.png 1. Estimate the conditional distributions from 'old' data (e.g., latencies before deployment): :math:`P_{X_1, ..., X_n} = \prod_j P_{X_j | PA_j}`, where :math:`P_{X_j | PA_j}` is the causal mechanism of node :math:`X_j` and :math:`PA_j` the parents of node :math:`X_j` 2. Estimate the conditional distributions from 'new' data (e.g., latencies after deployment): :math:`\tilde P_{X_1, ..., X_n} = \prod_j \tilde P_{X_j | PA_j}` 3. Replace mechanisms based on the 'old' data with mechanisms based on the 'new' data systematically, one by one. For this, replace :math:`P_{X_j | PA_j}` by :math:`\tilde P_{X_j | PA_j}` for each :math:`j`. If nodes in :math:`T \subseteq \{1, ..., n\}` have been replaced before, we get :math:`\tilde P^{X_n}_T = \sum_{x_1, ..., x_{n-1}} \prod_{j \in T} \tilde P_{X_j | PA_j} \prod_{j \notin T} P_{X_j | PA_j}`, a new marginal for node :math:`n`. 4. Attribute the change in the marginal given :math:`T` to :math:`X_j` using Shapley values by comparing :math:`P^{X_n}_{T \bigcup \{j\}}` and :math:`P^{X_n}_{T}`. Here, we can use different measures to capture the change, such as KL divergence to the original distribution or difference in variances etc. For more detailed explanation, see the corresponding paper: `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_

bloebp

12168ea7bd7a30d4c0d6501f69c7161ddb073845

5d449be765fbb04d77a35d2ace7978bfc6d90309

It would be more accurate to say "Estimate the conditional distributions from `old` data...".

kailashbuki

py-why/dowhy

Revise attributing distributional changes user guide entry

2023-02-17 22:20:40+00:00

2023-03-07 16:14:00+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/attribute_distributional_changes.rst

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: What mechanism in my system changed between two sets of data? For example, in a distributed computing system, we want to know why an important system metric changed in a negative way. How to use it ^^^^^^^^^^^^^^ To see how the method works, let's take the example from above and assume we have a system of three services X, Y, Z, producing latency numbers. The first dataset ``data_old`` is before the deployment, ``data_new`` is after the deployment: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=1, size=1000) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=1, size=1000) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) The change here simulates an accidental conversion of multi-threaded code into sequential one (waiting for X and Y in parallel vs. waiting for them sequentially). Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z')])) # X -> Z <- Y >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) Finally, we attribute changes in distributions to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'Z') >>> attributions {'X': -0.0066425020480165905, 'Y': 0.009816959724738061, 'Z': 0.21957816956354193} As we can see, :math:`Z` got the highest attribution score here, which matches what we would expect, given that we changed the mechanism for variable :math:`Z` in our data generation. As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset.

Attributing Distributional Changes ================================== When attributing distribution changes, we answer the question: **What mechanism in my system changed between two sets of data? Or in other words, which node in my data behaves differently?** Here we want to identify the node or nodes in the graph where the causal mechanism has changed. For example, if we detect an uptick in latency of our application within a microservice architecture, we aim to identify the node/component whose behavior has altered. has changed. DoWhy implements a method to identify and attribute changes in a distribution to changes in causal mechanisms of upstream nodes following the paper: Kailash Budhathoki, Dominik Janzing, Patrick Blöbaum, Hoiyi Ng. `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_ Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1666-1674, 2021. How to use it ^^^^^^^^^^^^^^ To see how to use the method, let's take the microservice example from above and assume we have a system of four services :math:`X, Y, Z, W`, each of which monitors latencies. Suppose we plan to carry out a new deployment and record the latencies before and after the deployment. We will refer to the latency data gathered prior to the deployment as ``data_old`` and the data gathered after the deployment as ``data_new``: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> from scipy.stats import halfnorm >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) >>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2) >>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2) >>> Z = X + Y + np.random.normal(loc=0, scale=0.5, size=1000) >>> W = Z + halfnorm.rvs(size=1000, loc=0.1, scale=0.2) >>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z, W=W)) Here, we change the behaviour of :math:`Z`, which simulates an accidental conversion of multi-threaded code into sequential one (waiting for :math:`X` and :math:`Y` in parallel vs. waiting for them sequentially). This will change the distribution of :math:`Z` and subsequently :math:`W`. Next, we'll model cause-effect relationships as a probabilistic causal model: >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Z'), ('Y', 'Z'), ('Z', 'W')])) # (X, Y) -> Z -> W >>> gcm.auto.assign_causal_mechanisms(causal_model, data_old) Finally, we attribute changes in distributions of :math:`W` to changes in causal mechanisms: >>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'W') >>> attributions {'W': 0.012553173521649849, 'X': -0.007493424287710609, 'Y': 0.0013256550695736396, 'Z': 0.7396701922473544} Although the distribution of :math:`W` has changed as well, the method attributes the change almost completely to :math:`Z` with negligible scores for the other variables. This is in line with our expectations since we only altered the mechanism of :math:`Z`. Note that the unit of the scores depends on the used measure (see the next section). As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call ``fit`` internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ The idea behind this method is to *systematically* replace the causal mechanism learned based on the old dataset with the mechanism learned based on the new dataset. After each replacement, new samples are generated for the target node, where the data generation process is a mixture of old and new mechanisms. Our goal is to identify the mechanisms that have changed, which would lead to a different marginal distribution of the target, while unchanged mechanisms would result in the same marginal distribution. To achieve this, we employ the idea of a Shapley symmetrization to systematically replace the mechanisms. This enables us to identify which nodes have changed and to estimate an attribution score with respect to some measure. Note that a change in the mechanism could be due to a functional change in the underlying model or a change in the (unobserved) noise distribution. However, both changes would lead to a change in the mechanism. The steps here are as follows: .. image:: dist_change.png 1. Estimate the conditional distributions from 'old' data (e.g., latencies before deployment): :math:`P_{X_1, ..., X_n} = \prod_j P_{X_j | PA_j}`, where :math:`P_{X_j | PA_j}` is the causal mechanism of node :math:`X_j` and :math:`PA_j` the parents of node :math:`X_j` 2. Estimate the conditional distributions from 'new' data (e.g., latencies after deployment): :math:`\tilde P_{X_1, ..., X_n} = \prod_j \tilde P_{X_j | PA_j}` 3. Replace mechanisms based on the 'old' data with mechanisms based on the 'new' data systematically, one by one. For this, replace :math:`P_{X_j | PA_j}` by :math:`\tilde P_{X_j | PA_j}` for each :math:`j`. If nodes in :math:`T \subseteq \{1, ..., n\}` have been replaced before, we get :math:`\tilde P^{X_n}_T = \sum_{x_1, ..., x_{n-1}} \prod_{j \in T} \tilde P_{X_j | PA_j} \prod_{j \notin T} P_{X_j | PA_j}`, a new marginal for node :math:`n`. 4. Attribute the change in the marginal given :math:`T` to :math:`X_j` using Shapley values by comparing :math:`P^{X_n}_{T \bigcup \{j\}}` and :math:`P^{X_n}_{T}`. Here, we can use different measures to capture the change, such as KL divergence to the original distribution or difference in variances etc. For more detailed explanation, see the corresponding paper: `Why did the distribution change? <http://proceedings.mlr.press/v130/budhathoki21a/budhathoki21a.pdf>`_

bloebp

12168ea7bd7a30d4c0d6501f69c7161ddb073845

5d449be765fbb04d77a35d2ace7978bfc6d90309

Replace old mechanisms with new one by one.

kailashbuki

py-why/dowhy

Revise gcm user guide entry for counterfactuals

2023-02-14 23:09:28+00:00

2023-03-07 16:14:22+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/computing_counterfactuals.rst

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome z for a variable Z where variable X was set to a value x. What would have happened to the value of Z, had I intervened on X to assign it a different value x'? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (Z=10). I didn't take any medication against it in recent months (X=0). What would have happened to my cholesterol LDL level (Z), had I taken a medication dosage of 5g a day (X := 5)? How to use it ^^^^^^^^^^^^^^ To see how the method works, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we'll model cause-effect relationships as an invertible SCM and fit it to the data: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Finally, let's compute the counterfactual when intervening on X: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> observed_data=pd.DataFrame(data=dict(X=[1], Y=[2], Z=[3]))) X Y Z 0 2 4.034229 9.073294 As we can see, :math:`X` takes our treatment-/intervention-value of 2, and :math:`Y` and :math:`Z` take deterministic values, based on our trained causal models and fixed observed data. I.e., based on the data generation process, if :math:`X = 1`, :math:`Y = 2`, we would expect :math:`Z` to be 6, but we *observed* :math:`Z = 3`, which means the particular noise value for :math:`Z` in this particular sample is approximately -2.98. Now, given that we know this hidden noise factor, we can estimate the counterfactual value of :math:`Z`, had we set :math:`X := 2`, which is approximately 9.07 (as can be seen in the result above). This shows that the observed data is used to calculate the noise data in the system. We can also provide these noise values directly, via: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[-0.007913], Z=[-2.97568]))) X Y Z 0 2 4.034229 9.073293 As we see, with :math:`X = 2` and :math:`Y \approx 4.03`, :math:`Z` should be approximately 12. But we know the hidden noise for this sample, approximately -2.98. So the counterfactual outcome is again :math:`Z \approx 9.07`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we generate all noise using our causal models. For counterfactuals, we use the noise from actual observed data. To expand on our example above, we assume there are other factors that contribute to cholesterol levels, e.g. exercising or genetic predisposition. While we *assume* medication helps against high LDL levels, it's important to take into account all other factors that could also help against it. We want to prove *what* has helped. Hence, it's important to use the noise from the real data, not some generated noise from our generative models. Otherwise, I may be able to reduce my cholesterol LDL level in the counterfactual world, where I take medication (X := 5), but not because I took the medication, but because the *generated noise* of Z also just happened to be low and so caused a low value for Z. By taking the *real* noise value of Z (derived from the observed data of Z), I can prove that it was the medication that helped.

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome :math:`z` for a variable :math:`Z` where variable :math:`X` was set to a value :math:`x`. What would have happened to the value of :math:`Z`, had I intervened on :math:`X` to assign it a different value :math:`x'`? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (:math:`Z = 10`). I didn't take any medication against it in recent months (:math:`x = 0`). What would have happened to my cholesterol LDL level (:math:`Z`), had I taken a medication dosage of 5g a day (:math:`X := 5`)? Note that the estimation of counterfactuals based on Pearl's graphical causal model framework requires stronger assumptions than the generation of interventional samples (see the :ref:`Understanding the method <understand-method>` section for more details). How to use it ^^^^^^^^^^^^^^ To see how we can use this method, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.uniform(low=0, high=10, size=1000) >>> Y = -2*X + np.random.normal(loc=0, scale=5, size=1000) >>> Z = 3*Y + 80 + np.random.normal(loc=0, scale=5, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) If we think of the cholesterol example, one could think of :math:`Y` here as some kind of body measurement that affects the cholesterol LDL level, such as a derivative of the body's ability to absorb the medication or its metabolism. Next, we'll model cause-effect relationships and fit the models to the data. Estimating counterfactuals requires an invertible SCM that can be represented by additive noise models: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Suppose we have observed the values :math:`x=0, y=5, z=110`. We are interested in knowing if taking medication, e.g., setting :math:`x:=5`, would have led to a smaller value for :math:`z`. The counterfactual value of :math:`z` for this scenario can be estimated in the following way: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> observed_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[110]))) X Y Z 0 5 -4.82026 80.62051 As we can see, :math:`X` takes our treatment-/intervention-value of 5, and :math:`Y` and :math:`Z` take deterministic values that are *based on our trained causal models* and the fixed observation. For example, if :math:`X` were 0 and :math:`Y` were 5, we would expect :math:`Z` to be 95 based on the data generation process. However, we observed :math:`Z` to be 110, indicating a noise value of approximately ~15 in this *particular* sample. With knowledge of this hidden noise factor, we can estimate the counterfactual value of :math:`Z` had we set :math:`X` to 5, which is approximately ~80 as shown in the result above. We can also provide these noise values directly to the function: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[15]))) X Y Z 0 5 -4.845684 80.431559 As we see, with :math:`X` set to 5 and :math:`y = -2 \cdot x + 5 = -5`, :math:`z` should be approximately ~65. But we know the hidden noise for :math:`Z` is approximately ~15. So the counterfactual outcome is again :math:`z = 3*y + 80 + 15 = 80`. It's important to note that the estimated values we obtained are not exact as we see in the results, since the model parameters were not learned perfectly. Specifically, the learned coefficients for :math:`Y` and :math:`Z` are not precisely -2 and 3, respectively, as suggested by the data generation process. As usual in machine learning, more data or fine-tuning models can help to improve accuracy. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals in graphical causal models are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we first recreate all noise values for a specific observation and then estimate the counterfactual outcome. However, this requires stronger modeling assumptions than generating interventional samples. Recall that the causal mechanism of a node :math:`Y` is represented as :math:`Y := f(X, N)`, where :math:`X` are the parents of :math:`Y` and :math:`N` is the noise. To generate interventional samples for :math:`Y`, we can take any random value from :math:`N`, but for counterfactuals, we need to first reconstruct the specific noise value (based on the model) that led to our observation. This requires the causal mechanism to be invertible with respect to :math:`N`, although it does not need to be invertible with respect to :math:`X`. A common modeling assumptions that ensures this are additive noise models of the form :math:`Y := f(X) + N`, where the noise can be reconstructed by :math:`N = Y - f(X)`. Note that currently only continuous data is supported for counterfactual estimation, while there is no restriction on the data type for generating interventional samples. To further clarify the role of the noise here, let's revisit the example in the introduction about high levels of cholesterol LDL. Seeing that there are many unobserved factors that can impact cholesterol levels, such as exercise and genetics, the question arises: If I had taken medication, would my LDL levels have been reduced? To answer this, we can use interventions where we keep the subject specific unobserved factors (i.e., noise) constant and only change the amount of hypothetically taken medicine. In practice this can be achieved by first reconstructing the noise and then use that specific value to estimate the LDL levels after intervening on the amount of medicine. Here it is crucial to use the reconstructed noise value rather than randomly sampling it from the noise distribution. Otherwise, one may see a reduction in LDL levels, not because of the medication itself, but because of the generated noise value that coincidentally causes low levels. Assuming the modeling assumptions are approximately correct, we can then analyze whether the medication would have helped in the counterfactual scenario. .. note:: **Remark on invertible mechanisms**: Generally, mechanisms that are invertible with respect to :math:`N` allow us to estimate point counterfactuals. However, it is also possible to allow some mechanisms to be non-invertible. In this case, however, we would obtain a counterfactual *distribution* based on the observational evidence, which may not necessarily be point-wise.

bloebp

5d449be765fbb04d77a35d2ace7978bfc6d90309

d7b7cc65c5b6780fbc0a32ec4cd9f94e17878353

1. The data generation process can be made more realistic. Currently, there can be negative dosages too (absurd!). 2. Should we also explain what Y is?

kailashbuki

py-why/dowhy

Revise gcm user guide entry for counterfactuals

2023-02-14 23:09:28+00:00

2023-03-07 16:14:22+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/computing_counterfactuals.rst

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome z for a variable Z where variable X was set to a value x. What would have happened to the value of Z, had I intervened on X to assign it a different value x'? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (Z=10). I didn't take any medication against it in recent months (X=0). What would have happened to my cholesterol LDL level (Z), had I taken a medication dosage of 5g a day (X := 5)? How to use it ^^^^^^^^^^^^^^ To see how the method works, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we'll model cause-effect relationships as an invertible SCM and fit it to the data: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Finally, let's compute the counterfactual when intervening on X: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> observed_data=pd.DataFrame(data=dict(X=[1], Y=[2], Z=[3]))) X Y Z 0 2 4.034229 9.073294 As we can see, :math:`X` takes our treatment-/intervention-value of 2, and :math:`Y` and :math:`Z` take deterministic values, based on our trained causal models and fixed observed data. I.e., based on the data generation process, if :math:`X = 1`, :math:`Y = 2`, we would expect :math:`Z` to be 6, but we *observed* :math:`Z = 3`, which means the particular noise value for :math:`Z` in this particular sample is approximately -2.98. Now, given that we know this hidden noise factor, we can estimate the counterfactual value of :math:`Z`, had we set :math:`X := 2`, which is approximately 9.07 (as can be seen in the result above). This shows that the observed data is used to calculate the noise data in the system. We can also provide these noise values directly, via: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[-0.007913], Z=[-2.97568]))) X Y Z 0 2 4.034229 9.073293 As we see, with :math:`X = 2` and :math:`Y \approx 4.03`, :math:`Z` should be approximately 12. But we know the hidden noise for this sample, approximately -2.98. So the counterfactual outcome is again :math:`Z \approx 9.07`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we generate all noise using our causal models. For counterfactuals, we use the noise from actual observed data. To expand on our example above, we assume there are other factors that contribute to cholesterol levels, e.g. exercising or genetic predisposition. While we *assume* medication helps against high LDL levels, it's important to take into account all other factors that could also help against it. We want to prove *what* has helped. Hence, it's important to use the noise from the real data, not some generated noise from our generative models. Otherwise, I may be able to reduce my cholesterol LDL level in the counterfactual world, where I take medication (X := 5), but not because I took the medication, but because the *generated noise* of Z also just happened to be low and so caused a low value for Z. By taking the *real* noise value of Z (derived from the observed data of Z), I can prove that it was the medication that helped.

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome :math:`z` for a variable :math:`Z` where variable :math:`X` was set to a value :math:`x`. What would have happened to the value of :math:`Z`, had I intervened on :math:`X` to assign it a different value :math:`x'`? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (:math:`Z = 10`). I didn't take any medication against it in recent months (:math:`x = 0`). What would have happened to my cholesterol LDL level (:math:`Z`), had I taken a medication dosage of 5g a day (:math:`X := 5`)? Note that the estimation of counterfactuals based on Pearl's graphical causal model framework requires stronger assumptions than the generation of interventional samples (see the :ref:`Understanding the method <understand-method>` section for more details). How to use it ^^^^^^^^^^^^^^ To see how we can use this method, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.uniform(low=0, high=10, size=1000) >>> Y = -2*X + np.random.normal(loc=0, scale=5, size=1000) >>> Z = 3*Y + 80 + np.random.normal(loc=0, scale=5, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) If we think of the cholesterol example, one could think of :math:`Y` here as some kind of body measurement that affects the cholesterol LDL level, such as a derivative of the body's ability to absorb the medication or its metabolism. Next, we'll model cause-effect relationships and fit the models to the data. Estimating counterfactuals requires an invertible SCM that can be represented by additive noise models: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Suppose we have observed the values :math:`x=0, y=5, z=110`. We are interested in knowing if taking medication, e.g., setting :math:`x:=5`, would have led to a smaller value for :math:`z`. The counterfactual value of :math:`z` for this scenario can be estimated in the following way: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> observed_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[110]))) X Y Z 0 5 -4.82026 80.62051 As we can see, :math:`X` takes our treatment-/intervention-value of 5, and :math:`Y` and :math:`Z` take deterministic values that are *based on our trained causal models* and the fixed observation. For example, if :math:`X` were 0 and :math:`Y` were 5, we would expect :math:`Z` to be 95 based on the data generation process. However, we observed :math:`Z` to be 110, indicating a noise value of approximately ~15 in this *particular* sample. With knowledge of this hidden noise factor, we can estimate the counterfactual value of :math:`Z` had we set :math:`X` to 5, which is approximately ~80 as shown in the result above. We can also provide these noise values directly to the function: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[15]))) X Y Z 0 5 -4.845684 80.431559 As we see, with :math:`X` set to 5 and :math:`y = -2 \cdot x + 5 = -5`, :math:`z` should be approximately ~65. But we know the hidden noise for :math:`Z` is approximately ~15. So the counterfactual outcome is again :math:`z = 3*y + 80 + 15 = 80`. It's important to note that the estimated values we obtained are not exact as we see in the results, since the model parameters were not learned perfectly. Specifically, the learned coefficients for :math:`Y` and :math:`Z` are not precisely -2 and 3, respectively, as suggested by the data generation process. As usual in machine learning, more data or fine-tuning models can help to improve accuracy. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals in graphical causal models are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we first recreate all noise values for a specific observation and then estimate the counterfactual outcome. However, this requires stronger modeling assumptions than generating interventional samples. Recall that the causal mechanism of a node :math:`Y` is represented as :math:`Y := f(X, N)`, where :math:`X` are the parents of :math:`Y` and :math:`N` is the noise. To generate interventional samples for :math:`Y`, we can take any random value from :math:`N`, but for counterfactuals, we need to first reconstruct the specific noise value (based on the model) that led to our observation. This requires the causal mechanism to be invertible with respect to :math:`N`, although it does not need to be invertible with respect to :math:`X`. A common modeling assumptions that ensures this are additive noise models of the form :math:`Y := f(X) + N`, where the noise can be reconstructed by :math:`N = Y - f(X)`. Note that currently only continuous data is supported for counterfactual estimation, while there is no restriction on the data type for generating interventional samples. To further clarify the role of the noise here, let's revisit the example in the introduction about high levels of cholesterol LDL. Seeing that there are many unobserved factors that can impact cholesterol levels, such as exercise and genetics, the question arises: If I had taken medication, would my LDL levels have been reduced? To answer this, we can use interventions where we keep the subject specific unobserved factors (i.e., noise) constant and only change the amount of hypothetically taken medicine. In practice this can be achieved by first reconstructing the noise and then use that specific value to estimate the LDL levels after intervening on the amount of medicine. Here it is crucial to use the reconstructed noise value rather than randomly sampling it from the noise distribution. Otherwise, one may see a reduction in LDL levels, not because of the medication itself, but because of the generated noise value that coincidentally causes low levels. Assuming the modeling assumptions are approximately correct, we can then analyze whether the medication would have helped in the counterfactual scenario. .. note:: **Remark on invertible mechanisms**: Generally, mechanisms that are invertible with respect to :math:`N` allow us to estimate point counterfactuals. However, it is also possible to allow some mechanisms to be non-invertible. In this case, however, we would obtain a counterfactual *distribution* based on the observational evidence, which may not necessarily be point-wise.

bloebp

5d449be765fbb04d77a35d2ace7978bfc6d90309

d7b7cc65c5b6780fbc0a32ec4cd9f94e17878353

I would replace "when intervening on ..." with "had we intervened on ...". Reads better. Clearly states we are contemplating about the past.

kailashbuki

py-why/dowhy

Revise gcm user guide entry for counterfactuals

2023-02-14 23:09:28+00:00

2023-03-07 16:14:22+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/computing_counterfactuals.rst

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome z for a variable Z where variable X was set to a value x. What would have happened to the value of Z, had I intervened on X to assign it a different value x'? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (Z=10). I didn't take any medication against it in recent months (X=0). What would have happened to my cholesterol LDL level (Z), had I taken a medication dosage of 5g a day (X := 5)? How to use it ^^^^^^^^^^^^^^ To see how the method works, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we'll model cause-effect relationships as an invertible SCM and fit it to the data: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Finally, let's compute the counterfactual when intervening on X: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> observed_data=pd.DataFrame(data=dict(X=[1], Y=[2], Z=[3]))) X Y Z 0 2 4.034229 9.073294 As we can see, :math:`X` takes our treatment-/intervention-value of 2, and :math:`Y` and :math:`Z` take deterministic values, based on our trained causal models and fixed observed data. I.e., based on the data generation process, if :math:`X = 1`, :math:`Y = 2`, we would expect :math:`Z` to be 6, but we *observed* :math:`Z = 3`, which means the particular noise value for :math:`Z` in this particular sample is approximately -2.98. Now, given that we know this hidden noise factor, we can estimate the counterfactual value of :math:`Z`, had we set :math:`X := 2`, which is approximately 9.07 (as can be seen in the result above). This shows that the observed data is used to calculate the noise data in the system. We can also provide these noise values directly, via: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[-0.007913], Z=[-2.97568]))) X Y Z 0 2 4.034229 9.073293 As we see, with :math:`X = 2` and :math:`Y \approx 4.03`, :math:`Z` should be approximately 12. But we know the hidden noise for this sample, approximately -2.98. So the counterfactual outcome is again :math:`Z \approx 9.07`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we generate all noise using our causal models. For counterfactuals, we use the noise from actual observed data. To expand on our example above, we assume there are other factors that contribute to cholesterol levels, e.g. exercising or genetic predisposition. While we *assume* medication helps against high LDL levels, it's important to take into account all other factors that could also help against it. We want to prove *what* has helped. Hence, it's important to use the noise from the real data, not some generated noise from our generative models. Otherwise, I may be able to reduce my cholesterol LDL level in the counterfactual world, where I take medication (X := 5), but not because I took the medication, but because the *generated noise* of Z also just happened to be low and so caused a low value for Z. By taking the *real* noise value of Z (derived from the observed data of Z), I can prove that it was the medication that helped.

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome :math:`z` for a variable :math:`Z` where variable :math:`X` was set to a value :math:`x`. What would have happened to the value of :math:`Z`, had I intervened on :math:`X` to assign it a different value :math:`x'`? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (:math:`Z = 10`). I didn't take any medication against it in recent months (:math:`x = 0`). What would have happened to my cholesterol LDL level (:math:`Z`), had I taken a medication dosage of 5g a day (:math:`X := 5`)? Note that the estimation of counterfactuals based on Pearl's graphical causal model framework requires stronger assumptions than the generation of interventional samples (see the :ref:`Understanding the method <understand-method>` section for more details). How to use it ^^^^^^^^^^^^^^ To see how we can use this method, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.uniform(low=0, high=10, size=1000) >>> Y = -2*X + np.random.normal(loc=0, scale=5, size=1000) >>> Z = 3*Y + 80 + np.random.normal(loc=0, scale=5, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) If we think of the cholesterol example, one could think of :math:`Y` here as some kind of body measurement that affects the cholesterol LDL level, such as a derivative of the body's ability to absorb the medication or its metabolism. Next, we'll model cause-effect relationships and fit the models to the data. Estimating counterfactuals requires an invertible SCM that can be represented by additive noise models: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Suppose we have observed the values :math:`x=0, y=5, z=110`. We are interested in knowing if taking medication, e.g., setting :math:`x:=5`, would have led to a smaller value for :math:`z`. The counterfactual value of :math:`z` for this scenario can be estimated in the following way: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> observed_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[110]))) X Y Z 0 5 -4.82026 80.62051 As we can see, :math:`X` takes our treatment-/intervention-value of 5, and :math:`Y` and :math:`Z` take deterministic values that are *based on our trained causal models* and the fixed observation. For example, if :math:`X` were 0 and :math:`Y` were 5, we would expect :math:`Z` to be 95 based on the data generation process. However, we observed :math:`Z` to be 110, indicating a noise value of approximately ~15 in this *particular* sample. With knowledge of this hidden noise factor, we can estimate the counterfactual value of :math:`Z` had we set :math:`X` to 5, which is approximately ~80 as shown in the result above. We can also provide these noise values directly to the function: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[15]))) X Y Z 0 5 -4.845684 80.431559 As we see, with :math:`X` set to 5 and :math:`y = -2 \cdot x + 5 = -5`, :math:`z` should be approximately ~65. But we know the hidden noise for :math:`Z` is approximately ~15. So the counterfactual outcome is again :math:`z = 3*y + 80 + 15 = 80`. It's important to note that the estimated values we obtained are not exact as we see in the results, since the model parameters were not learned perfectly. Specifically, the learned coefficients for :math:`Y` and :math:`Z` are not precisely -2 and 3, respectively, as suggested by the data generation process. As usual in machine learning, more data or fine-tuning models can help to improve accuracy. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals in graphical causal models are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we first recreate all noise values for a specific observation and then estimate the counterfactual outcome. However, this requires stronger modeling assumptions than generating interventional samples. Recall that the causal mechanism of a node :math:`Y` is represented as :math:`Y := f(X, N)`, where :math:`X` are the parents of :math:`Y` and :math:`N` is the noise. To generate interventional samples for :math:`Y`, we can take any random value from :math:`N`, but for counterfactuals, we need to first reconstruct the specific noise value (based on the model) that led to our observation. This requires the causal mechanism to be invertible with respect to :math:`N`, although it does not need to be invertible with respect to :math:`X`. A common modeling assumptions that ensures this are additive noise models of the form :math:`Y := f(X) + N`, where the noise can be reconstructed by :math:`N = Y - f(X)`. Note that currently only continuous data is supported for counterfactual estimation, while there is no restriction on the data type for generating interventional samples. To further clarify the role of the noise here, let's revisit the example in the introduction about high levels of cholesterol LDL. Seeing that there are many unobserved factors that can impact cholesterol levels, such as exercise and genetics, the question arises: If I had taken medication, would my LDL levels have been reduced? To answer this, we can use interventions where we keep the subject specific unobserved factors (i.e., noise) constant and only change the amount of hypothetically taken medicine. In practice this can be achieved by first reconstructing the noise and then use that specific value to estimate the LDL levels after intervening on the amount of medicine. Here it is crucial to use the reconstructed noise value rather than randomly sampling it from the noise distribution. Otherwise, one may see a reduction in LDL levels, not because of the medication itself, but because of the generated noise value that coincidentally causes low levels. Assuming the modeling assumptions are approximately correct, we can then analyze whether the medication would have helped in the counterfactual scenario. .. note:: **Remark on invertible mechanisms**: Generally, mechanisms that are invertible with respect to :math:`N` allow us to estimate point counterfactuals. However, it is also possible to allow some mechanisms to be non-invertible. In this case, however, we would obtain a counterfactual *distribution* based on the observational evidence, which may not necessarily be point-wise.

bloebp

5d449be765fbb04d77a35d2ace7978bfc6d90309

d7b7cc65c5b6780fbc0a32ec4cd9f94e17878353

Invertibility leads to point counterfactuals. But we may also have distributional counterfactuals, where we estimate the posterior distribution of noise terms given the observational evidence. We should make the latter explicit here as most readers of Pearl are familiar with the notion of distributional counterfactuals.

kailashbuki

py-why/dowhy

Revise gcm user guide entry for counterfactuals

2023-02-14 23:09:28+00:00

2023-03-07 16:14:22+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/computing_counterfactuals.rst

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome z for a variable Z where variable X was set to a value x. What would have happened to the value of Z, had I intervened on X to assign it a different value x'? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (Z=10). I didn't take any medication against it in recent months (X=0). What would have happened to my cholesterol LDL level (Z), had I taken a medication dosage of 5g a day (X := 5)? How to use it ^^^^^^^^^^^^^^ To see how the method works, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we'll model cause-effect relationships as an invertible SCM and fit it to the data: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Finally, let's compute the counterfactual when intervening on X: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> observed_data=pd.DataFrame(data=dict(X=[1], Y=[2], Z=[3]))) X Y Z 0 2 4.034229 9.073294 As we can see, :math:`X` takes our treatment-/intervention-value of 2, and :math:`Y` and :math:`Z` take deterministic values, based on our trained causal models and fixed observed data. I.e., based on the data generation process, if :math:`X = 1`, :math:`Y = 2`, we would expect :math:`Z` to be 6, but we *observed* :math:`Z = 3`, which means the particular noise value for :math:`Z` in this particular sample is approximately -2.98. Now, given that we know this hidden noise factor, we can estimate the counterfactual value of :math:`Z`, had we set :math:`X := 2`, which is approximately 9.07 (as can be seen in the result above). This shows that the observed data is used to calculate the noise data in the system. We can also provide these noise values directly, via: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[-0.007913], Z=[-2.97568]))) X Y Z 0 2 4.034229 9.073293 As we see, with :math:`X = 2` and :math:`Y \approx 4.03`, :math:`Z` should be approximately 12. But we know the hidden noise for this sample, approximately -2.98. So the counterfactual outcome is again :math:`Z \approx 9.07`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we generate all noise using our causal models. For counterfactuals, we use the noise from actual observed data. To expand on our example above, we assume there are other factors that contribute to cholesterol levels, e.g. exercising or genetic predisposition. While we *assume* medication helps against high LDL levels, it's important to take into account all other factors that could also help against it. We want to prove *what* has helped. Hence, it's important to use the noise from the real data, not some generated noise from our generative models. Otherwise, I may be able to reduce my cholesterol LDL level in the counterfactual world, where I take medication (X := 5), but not because I took the medication, but because the *generated noise* of Z also just happened to be low and so caused a low value for Z. By taking the *real* noise value of Z (derived from the observed data of Z), I can prove that it was the medication that helped.

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome :math:`z` for a variable :math:`Z` where variable :math:`X` was set to a value :math:`x`. What would have happened to the value of :math:`Z`, had I intervened on :math:`X` to assign it a different value :math:`x'`? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (:math:`Z = 10`). I didn't take any medication against it in recent months (:math:`x = 0`). What would have happened to my cholesterol LDL level (:math:`Z`), had I taken a medication dosage of 5g a day (:math:`X := 5`)? Note that the estimation of counterfactuals based on Pearl's graphical causal model framework requires stronger assumptions than the generation of interventional samples (see the :ref:`Understanding the method <understand-method>` section for more details). How to use it ^^^^^^^^^^^^^^ To see how we can use this method, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.uniform(low=0, high=10, size=1000) >>> Y = -2*X + np.random.normal(loc=0, scale=5, size=1000) >>> Z = 3*Y + 80 + np.random.normal(loc=0, scale=5, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) If we think of the cholesterol example, one could think of :math:`Y` here as some kind of body measurement that affects the cholesterol LDL level, such as a derivative of the body's ability to absorb the medication or its metabolism. Next, we'll model cause-effect relationships and fit the models to the data. Estimating counterfactuals requires an invertible SCM that can be represented by additive noise models: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Suppose we have observed the values :math:`x=0, y=5, z=110`. We are interested in knowing if taking medication, e.g., setting :math:`x:=5`, would have led to a smaller value for :math:`z`. The counterfactual value of :math:`z` for this scenario can be estimated in the following way: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> observed_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[110]))) X Y Z 0 5 -4.82026 80.62051 As we can see, :math:`X` takes our treatment-/intervention-value of 5, and :math:`Y` and :math:`Z` take deterministic values that are *based on our trained causal models* and the fixed observation. For example, if :math:`X` were 0 and :math:`Y` were 5, we would expect :math:`Z` to be 95 based on the data generation process. However, we observed :math:`Z` to be 110, indicating a noise value of approximately ~15 in this *particular* sample. With knowledge of this hidden noise factor, we can estimate the counterfactual value of :math:`Z` had we set :math:`X` to 5, which is approximately ~80 as shown in the result above. We can also provide these noise values directly to the function: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[15]))) X Y Z 0 5 -4.845684 80.431559 As we see, with :math:`X` set to 5 and :math:`y = -2 \cdot x + 5 = -5`, :math:`z` should be approximately ~65. But we know the hidden noise for :math:`Z` is approximately ~15. So the counterfactual outcome is again :math:`z = 3*y + 80 + 15 = 80`. It's important to note that the estimated values we obtained are not exact as we see in the results, since the model parameters were not learned perfectly. Specifically, the learned coefficients for :math:`Y` and :math:`Z` are not precisely -2 and 3, respectively, as suggested by the data generation process. As usual in machine learning, more data or fine-tuning models can help to improve accuracy. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals in graphical causal models are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we first recreate all noise values for a specific observation and then estimate the counterfactual outcome. However, this requires stronger modeling assumptions than generating interventional samples. Recall that the causal mechanism of a node :math:`Y` is represented as :math:`Y := f(X, N)`, where :math:`X` are the parents of :math:`Y` and :math:`N` is the noise. To generate interventional samples for :math:`Y`, we can take any random value from :math:`N`, but for counterfactuals, we need to first reconstruct the specific noise value (based on the model) that led to our observation. This requires the causal mechanism to be invertible with respect to :math:`N`, although it does not need to be invertible with respect to :math:`X`. A common modeling assumptions that ensures this are additive noise models of the form :math:`Y := f(X) + N`, where the noise can be reconstructed by :math:`N = Y - f(X)`. Note that currently only continuous data is supported for counterfactual estimation, while there is no restriction on the data type for generating interventional samples. To further clarify the role of the noise here, let's revisit the example in the introduction about high levels of cholesterol LDL. Seeing that there are many unobserved factors that can impact cholesterol levels, such as exercise and genetics, the question arises: If I had taken medication, would my LDL levels have been reduced? To answer this, we can use interventions where we keep the subject specific unobserved factors (i.e., noise) constant and only change the amount of hypothetically taken medicine. In practice this can be achieved by first reconstructing the noise and then use that specific value to estimate the LDL levels after intervening on the amount of medicine. Here it is crucial to use the reconstructed noise value rather than randomly sampling it from the noise distribution. Otherwise, one may see a reduction in LDL levels, not because of the medication itself, but because of the generated noise value that coincidentally causes low levels. Assuming the modeling assumptions are approximately correct, we can then analyze whether the medication would have helped in the counterfactual scenario. .. note:: **Remark on invertible mechanisms**: Generally, mechanisms that are invertible with respect to :math:`N` allow us to estimate point counterfactuals. However, it is also possible to allow some mechanisms to be non-invertible. In this case, however, we would obtain a counterfactual *distribution* based on the observational evidence, which may not necessarily be point-wise.

bloebp

5d449be765fbb04d77a35d2ace7978bfc6d90309

d7b7cc65c5b6780fbc0a32ec4cd9f94e17878353

I completely rewrote the example to keep it connected to the cholesterol example while being somewhat 'realistic'.

bloebp

py-why/dowhy

Revise gcm user guide entry for counterfactuals

2023-02-14 23:09:28+00:00

2023-03-07 16:14:22+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/computing_counterfactuals.rst

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome z for a variable Z where variable X was set to a value x. What would have happened to the value of Z, had I intervened on X to assign it a different value x'? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (Z=10). I didn't take any medication against it in recent months (X=0). What would have happened to my cholesterol LDL level (Z), had I taken a medication dosage of 5g a day (X := 5)? How to use it ^^^^^^^^^^^^^^ To see how the method works, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we'll model cause-effect relationships as an invertible SCM and fit it to the data: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Finally, let's compute the counterfactual when intervening on X: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> observed_data=pd.DataFrame(data=dict(X=[1], Y=[2], Z=[3]))) X Y Z 0 2 4.034229 9.073294 As we can see, :math:`X` takes our treatment-/intervention-value of 2, and :math:`Y` and :math:`Z` take deterministic values, based on our trained causal models and fixed observed data. I.e., based on the data generation process, if :math:`X = 1`, :math:`Y = 2`, we would expect :math:`Z` to be 6, but we *observed* :math:`Z = 3`, which means the particular noise value for :math:`Z` in this particular sample is approximately -2.98. Now, given that we know this hidden noise factor, we can estimate the counterfactual value of :math:`Z`, had we set :math:`X := 2`, which is approximately 9.07 (as can be seen in the result above). This shows that the observed data is used to calculate the noise data in the system. We can also provide these noise values directly, via: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[-0.007913], Z=[-2.97568]))) X Y Z 0 2 4.034229 9.073293 As we see, with :math:`X = 2` and :math:`Y \approx 4.03`, :math:`Z` should be approximately 12. But we know the hidden noise for this sample, approximately -2.98. So the counterfactual outcome is again :math:`Z \approx 9.07`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we generate all noise using our causal models. For counterfactuals, we use the noise from actual observed data. To expand on our example above, we assume there are other factors that contribute to cholesterol levels, e.g. exercising or genetic predisposition. While we *assume* medication helps against high LDL levels, it's important to take into account all other factors that could also help against it. We want to prove *what* has helped. Hence, it's important to use the noise from the real data, not some generated noise from our generative models. Otherwise, I may be able to reduce my cholesterol LDL level in the counterfactual world, where I take medication (X := 5), but not because I took the medication, but because the *generated noise* of Z also just happened to be low and so caused a low value for Z. By taking the *real* noise value of Z (derived from the observed data of Z), I can prove that it was the medication that helped.

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome :math:`z` for a variable :math:`Z` where variable :math:`X` was set to a value :math:`x`. What would have happened to the value of :math:`Z`, had I intervened on :math:`X` to assign it a different value :math:`x'`? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (:math:`Z = 10`). I didn't take any medication against it in recent months (:math:`x = 0`). What would have happened to my cholesterol LDL level (:math:`Z`), had I taken a medication dosage of 5g a day (:math:`X := 5`)? Note that the estimation of counterfactuals based on Pearl's graphical causal model framework requires stronger assumptions than the generation of interventional samples (see the :ref:`Understanding the method <understand-method>` section for more details). How to use it ^^^^^^^^^^^^^^ To see how we can use this method, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.uniform(low=0, high=10, size=1000) >>> Y = -2*X + np.random.normal(loc=0, scale=5, size=1000) >>> Z = 3*Y + 80 + np.random.normal(loc=0, scale=5, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) If we think of the cholesterol example, one could think of :math:`Y` here as some kind of body measurement that affects the cholesterol LDL level, such as a derivative of the body's ability to absorb the medication or its metabolism. Next, we'll model cause-effect relationships and fit the models to the data. Estimating counterfactuals requires an invertible SCM that can be represented by additive noise models: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Suppose we have observed the values :math:`x=0, y=5, z=110`. We are interested in knowing if taking medication, e.g., setting :math:`x:=5`, would have led to a smaller value for :math:`z`. The counterfactual value of :math:`z` for this scenario can be estimated in the following way: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> observed_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[110]))) X Y Z 0 5 -4.82026 80.62051 As we can see, :math:`X` takes our treatment-/intervention-value of 5, and :math:`Y` and :math:`Z` take deterministic values that are *based on our trained causal models* and the fixed observation. For example, if :math:`X` were 0 and :math:`Y` were 5, we would expect :math:`Z` to be 95 based on the data generation process. However, we observed :math:`Z` to be 110, indicating a noise value of approximately ~15 in this *particular* sample. With knowledge of this hidden noise factor, we can estimate the counterfactual value of :math:`Z` had we set :math:`X` to 5, which is approximately ~80 as shown in the result above. We can also provide these noise values directly to the function: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[15]))) X Y Z 0 5 -4.845684 80.431559 As we see, with :math:`X` set to 5 and :math:`y = -2 \cdot x + 5 = -5`, :math:`z` should be approximately ~65. But we know the hidden noise for :math:`Z` is approximately ~15. So the counterfactual outcome is again :math:`z = 3*y + 80 + 15 = 80`. It's important to note that the estimated values we obtained are not exact as we see in the results, since the model parameters were not learned perfectly. Specifically, the learned coefficients for :math:`Y` and :math:`Z` are not precisely -2 and 3, respectively, as suggested by the data generation process. As usual in machine learning, more data or fine-tuning models can help to improve accuracy. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals in graphical causal models are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we first recreate all noise values for a specific observation and then estimate the counterfactual outcome. However, this requires stronger modeling assumptions than generating interventional samples. Recall that the causal mechanism of a node :math:`Y` is represented as :math:`Y := f(X, N)`, where :math:`X` are the parents of :math:`Y` and :math:`N` is the noise. To generate interventional samples for :math:`Y`, we can take any random value from :math:`N`, but for counterfactuals, we need to first reconstruct the specific noise value (based on the model) that led to our observation. This requires the causal mechanism to be invertible with respect to :math:`N`, although it does not need to be invertible with respect to :math:`X`. A common modeling assumptions that ensures this are additive noise models of the form :math:`Y := f(X) + N`, where the noise can be reconstructed by :math:`N = Y - f(X)`. Note that currently only continuous data is supported for counterfactual estimation, while there is no restriction on the data type for generating interventional samples. To further clarify the role of the noise here, let's revisit the example in the introduction about high levels of cholesterol LDL. Seeing that there are many unobserved factors that can impact cholesterol levels, such as exercise and genetics, the question arises: If I had taken medication, would my LDL levels have been reduced? To answer this, we can use interventions where we keep the subject specific unobserved factors (i.e., noise) constant and only change the amount of hypothetically taken medicine. In practice this can be achieved by first reconstructing the noise and then use that specific value to estimate the LDL levels after intervening on the amount of medicine. Here it is crucial to use the reconstructed noise value rather than randomly sampling it from the noise distribution. Otherwise, one may see a reduction in LDL levels, not because of the medication itself, but because of the generated noise value that coincidentally causes low levels. Assuming the modeling assumptions are approximately correct, we can then analyze whether the medication would have helped in the counterfactual scenario. .. note:: **Remark on invertible mechanisms**: Generally, mechanisms that are invertible with respect to :math:`N` allow us to estimate point counterfactuals. However, it is also possible to allow some mechanisms to be non-invertible. In this case, however, we would obtain a counterfactual *distribution* based on the observational evidence, which may not necessarily be point-wise.

bloebp

5d449be765fbb04d77a35d2ace7978bfc6d90309

d7b7cc65c5b6780fbc0a32ec4cd9f94e17878353

This sentence changed in the new version.

bloebp

py-why/dowhy

Revise gcm user guide entry for counterfactuals

2023-02-14 23:09:28+00:00

2023-03-07 16:14:22+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/computing_counterfactuals.rst

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome z for a variable Z where variable X was set to a value x. What would have happened to the value of Z, had I intervened on X to assign it a different value x'? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (Z=10). I didn't take any medication against it in recent months (X=0). What would have happened to my cholesterol LDL level (Z), had I taken a medication dosage of 5g a day (X := 5)? How to use it ^^^^^^^^^^^^^^ To see how the method works, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.normal(loc=0, scale=1, size=1000) >>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000) >>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) Next, we'll model cause-effect relationships as an invertible SCM and fit it to the data: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Finally, let's compute the counterfactual when intervening on X: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> observed_data=pd.DataFrame(data=dict(X=[1], Y=[2], Z=[3]))) X Y Z 0 2 4.034229 9.073294 As we can see, :math:`X` takes our treatment-/intervention-value of 2, and :math:`Y` and :math:`Z` take deterministic values, based on our trained causal models and fixed observed data. I.e., based on the data generation process, if :math:`X = 1`, :math:`Y = 2`, we would expect :math:`Z` to be 6, but we *observed* :math:`Z = 3`, which means the particular noise value for :math:`Z` in this particular sample is approximately -2.98. Now, given that we know this hidden noise factor, we can estimate the counterfactual value of :math:`Z`, had we set :math:`X := 2`, which is approximately 9.07 (as can be seen in the result above). This shows that the observed data is used to calculate the noise data in the system. We can also provide these noise values directly, via: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 2}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[-0.007913], Z=[-2.97568]))) X Y Z 0 2 4.034229 9.073293 As we see, with :math:`X = 2` and :math:`Y \approx 4.03`, :math:`Z` should be approximately 12. But we know the hidden noise for this sample, approximately -2.98. So the counterfactual outcome is again :math:`Z \approx 9.07`. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we generate all noise using our causal models. For counterfactuals, we use the noise from actual observed data. To expand on our example above, we assume there are other factors that contribute to cholesterol levels, e.g. exercising or genetic predisposition. While we *assume* medication helps against high LDL levels, it's important to take into account all other factors that could also help against it. We want to prove *what* has helped. Hence, it's important to use the noise from the real data, not some generated noise from our generative models. Otherwise, I may be able to reduce my cholesterol LDL level in the counterfactual world, where I take medication (X := 5), but not because I took the medication, but because the *generated noise* of Z also just happened to be low and so caused a low value for Z. By taking the *real* noise value of Z (derived from the observed data of Z), I can prove that it was the medication that helped.

Computing Counterfactuals ========================== By computing counterfactuals, we answer the question: I observed a certain outcome :math:`z` for a variable :math:`Z` where variable :math:`X` was set to a value :math:`x`. What would have happened to the value of :math:`Z`, had I intervened on :math:`X` to assign it a different value :math:`x'`? As a concrete example, we can imagine the following: I'm seeing unhealthy high levels of my `cholesterol LDL <https://www.google.com/search?q=cholesterol+ldl>`_ (:math:`Z = 10`). I didn't take any medication against it in recent months (:math:`x = 0`). What would have happened to my cholesterol LDL level (:math:`Z`), had I taken a medication dosage of 5g a day (:math:`X := 5`)? Note that the estimation of counterfactuals based on Pearl's graphical causal model framework requires stronger assumptions than the generation of interventional samples (see the :ref:`Understanding the method <understand-method>` section for more details). How to use it ^^^^^^^^^^^^^^ To see how we can use this method, let's generate some data: >>> import networkx as nx, numpy as np, pandas as pd >>> from dowhy import gcm >>> X = np.random.uniform(low=0, high=10, size=1000) >>> Y = -2*X + np.random.normal(loc=0, scale=5, size=1000) >>> Z = 3*Y + 80 + np.random.normal(loc=0, scale=5, size=1000) >>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z)) If we think of the cholesterol example, one could think of :math:`Y` here as some kind of body measurement that affects the cholesterol LDL level, such as a derivative of the body's ability to absorb the medication or its metabolism. Next, we'll model cause-effect relationships and fit the models to the data. Estimating counterfactuals requires an invertible SCM that can be represented by additive noise models: >>> causal_model = gcm.InvertibleStructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z >>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, training_data) Suppose we have observed the values :math:`x=0, y=5, z=110`. We are interested in knowing if taking medication, e.g., setting :math:`x:=5`, would have led to a smaller value for :math:`z`. The counterfactual value of :math:`z` for this scenario can be estimated in the following way: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> observed_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[110]))) X Y Z 0 5 -4.82026 80.62051 As we can see, :math:`X` takes our treatment-/intervention-value of 5, and :math:`Y` and :math:`Z` take deterministic values that are *based on our trained causal models* and the fixed observation. For example, if :math:`X` were 0 and :math:`Y` were 5, we would expect :math:`Z` to be 95 based on the data generation process. However, we observed :math:`Z` to be 110, indicating a noise value of approximately ~15 in this *particular* sample. With knowledge of this hidden noise factor, we can estimate the counterfactual value of :math:`Z` had we set :math:`X` to 5, which is approximately ~80 as shown in the result above. We can also provide these noise values directly to the function: >>> gcm.counterfactual_samples( >>> causal_model, >>> {'X': lambda x: 5}, >>> noise_data=pd.DataFrame(data=dict(X=[0], Y=[5], Z=[15]))) X Y Z 0 5 -4.845684 80.431559 As we see, with :math:`X` set to 5 and :math:`y = -2 \cdot x + 5 = -5`, :math:`z` should be approximately ~65. But we know the hidden noise for :math:`Z` is approximately ~15. So the counterfactual outcome is again :math:`z = 3*y + 80 + 15 = 80`. It's important to note that the estimated values we obtained are not exact as we see in the results, since the model parameters were not learned perfectly. Specifically, the learned coefficients for :math:`Y` and :math:`Z` are not precisely -2 and 3, respectively, as suggested by the data generation process. As usual in machine learning, more data or fine-tuning models can help to improve accuracy. .. _understand-method: Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ Counterfactuals in graphical causal models are very similar to :doc:`simulate_impact_of_interventions`, with an important difference: when performing interventions, we look into the future, for counterfactuals we look into an alternative past. To reflect this in the computation, when performing interventions, we first recreate all noise values for a specific observation and then estimate the counterfactual outcome. However, this requires stronger modeling assumptions than generating interventional samples. Recall that the causal mechanism of a node :math:`Y` is represented as :math:`Y := f(X, N)`, where :math:`X` are the parents of :math:`Y` and :math:`N` is the noise. To generate interventional samples for :math:`Y`, we can take any random value from :math:`N`, but for counterfactuals, we need to first reconstruct the specific noise value (based on the model) that led to our observation. This requires the causal mechanism to be invertible with respect to :math:`N`, although it does not need to be invertible with respect to :math:`X`. A common modeling assumptions that ensures this are additive noise models of the form :math:`Y := f(X) + N`, where the noise can be reconstructed by :math:`N = Y - f(X)`. Note that currently only continuous data is supported for counterfactual estimation, while there is no restriction on the data type for generating interventional samples. To further clarify the role of the noise here, let's revisit the example in the introduction about high levels of cholesterol LDL. Seeing that there are many unobserved factors that can impact cholesterol levels, such as exercise and genetics, the question arises: If I had taken medication, would my LDL levels have been reduced? To answer this, we can use interventions where we keep the subject specific unobserved factors (i.e., noise) constant and only change the amount of hypothetically taken medicine. In practice this can be achieved by first reconstructing the noise and then use that specific value to estimate the LDL levels after intervening on the amount of medicine. Here it is crucial to use the reconstructed noise value rather than randomly sampling it from the noise distribution. Otherwise, one may see a reduction in LDL levels, not because of the medication itself, but because of the generated noise value that coincidentally causes low levels. Assuming the modeling assumptions are approximately correct, we can then analyze whether the medication would have helped in the counterfactual scenario. .. note:: **Remark on invertible mechanisms**: Generally, mechanisms that are invertible with respect to :math:`N` allow us to estimate point counterfactuals. However, it is also possible to allow some mechanisms to be non-invertible. In this case, however, we would obtain a counterfactual *distribution* based on the observational evidence, which may not necessarily be point-wise.

bloebp

5d449be765fbb04d77a35d2ace7978bfc6d90309

d7b7cc65c5b6780fbc0a32ec4cd9f94e17878353

Good point, I added a note at the bottom. Allowing counterfactual distributions (beyond point-wise) is anyway something high on the todo list.

bloebp

py-why/dowhy

Revise arrow strength user guide

Signed-off-by: Patrick Bloebaum <bloebp@amazon.com>

2023-02-13 21:29:38+00:00

2023-03-07 16:14:39+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/quantify_arrow_strength.rst

Quantifying Arrow Strength ================================= By quantifying the strength of an arrow, we answer the question: How strong is the causal influence from a cause to its direct effect? How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data. >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> np.random.seed(10) # to reproduce these results >>> Z = np.random.normal(loc=0, scale=1, size=1000) >>> X = 2*Z + np.random.normal(loc=0, scale=1, size=1000) >>> Y = 3*X + 4*Z + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) Next, we will model cause-effect relationships as a probabilistic causal model and fit it to the data. >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('Z', 'Y'), ('Z', 'X'), ('X', 'Y')])) >>> causal_model.set_causal_mechanism('Z', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('X', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, data) Finally, we can estimate the strength of incoming arrows to a node of interest (e.g., :math:`Y`). >>> strength = gcm.arrow_strength(causal_model, 'Y') >>> strength {('X', 'Y'): 41.321925893102716, ('Z', 'Y'): 14.736197949517237} **Interpreting the results:** By default, the measurement unit of the scalar values for arrow strengths is variance for a continuous real-valued target, and the number of bits for a categorical target. Above, we observe that the direct influence from :math:`X` to :math:`Y` (~41.32) is stronger (by ~2.7 times) than the direct influence from :math:`Z` to :math:`Y` (~14.73). Roughly speaking, "removing" the arrow from :math:`X` to :math:`Y` increases the variance of :math:`Y` by ~41.32 units, whereas removing :math:`Z \to Y` increases the variance of :math:`Y` by ~14.73 units. In the next section, we explain what "removing" an edge implies. In particular, we briefly explain the science behind our method for quantifying the strength of an arrow. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ We will use the causal graph below to illustrate the key idea behind our method. .. image:: arrow_strength_example.png Recall that we can obtain the joint distribution of variables :math:`P` from their causal graph via a product of conditional distributions of each variable given its parents. To quantify the strength of an arrow from :math:`Z` to :math:`Y`, we define a new joint distribution :math:`P_{Z \to Y}`, also called post-cutting distribution, obtained by removing the edge :math:`Z \to Y`, and then feeding :math:`Y` with an i.i.d. copy of :math:`Z`. The i.i.d. copy can be simulated, in practice, by applying random permutation to samples of :math:`Z`. The strength of an arrow from :math:`Z` to :math:`Y`, denoted :math:`C_{Z \to Y}`, is then the distance (e.g., KL divergence) between the post-cutting distribution :math:`P_{Z \to Y}` and the original joint distribution :math:`P`. .. math:: C_{Z \to Y} := D_{\mathrm{KL}}(P\; || P_{Z \to Y}) Note that only the causal mechanism of the target variable (:math:`P_{Y \mid X, Z}` in the above example) changes between the original and the post-cutting joint distribution. Therefore, any change in the marginal distribution of the target (obtained by marginalising the joint distribution) is due to the change in the causal mechanism of the target variable. This means, we can also quantify the arrow strength in terms of the change in the property of the marginal distribution (e.g. mean, variance) of the target when we remove an edge. Measuring arrow strengths in different units ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ By default, `arrow_strength` employs KL divergence for measuring the arrow strength for categorical target, and difference in variance for continuous real-valued target. But we can also plug in our choice of measure, using the ``difference_estimation_func`` parameter. To measure the arrow strength in terms of the change in the mean, we could define: >>> def mean_diff(Y_old, Y_new): return np.mean(Y_new) - np.mean(Y_old) and then estimate the arrow strength: >>> gcm.arrow_strength(causal_model, 'Y', difference_estimation_func=mean_diff) {('X', 'Y'): 0.11898914602350251, ('Z', 'Y'): 0.07811542095834415} This is expected; in our example, the mean value of :math:`Y` remains :math:`0` regardless of whether we remove an incoming arrow. As such, the strength of incoming arrows to :math:`Y` should be negligible. In summary, arrow strength can be measured in different units (e.g., mean, variance, bits). Therefore, we advise users to pick a meaningful unit---based on data and interpretation---to apply this method in practice.

Quantifying Arrow Strength ================================= By quantifying the strength of an arrow, we answer the question: **How strong is the causal influence from a cause to its direct effect?** While there are different definitions for measuring causal influences in the literature, DoWhy offers an implementation for measuring the *direct* influence of a parent node on a child, where influences through paths over other nodes are ignored. This method is based on the paper: Dominik Janzing, David Balduzzi, Moritz Grosse-Wentrup, Bernhard Schölkopf. `Quantifying causal influences <https://www.jstor.org/stable/23566552>`_ The Annals of Statistics, Vol. 41, No. 5, 2324-2358, 2013. How to use it ^^^^^^^^^^^^^^ To see how to use the method, let us generate some data. >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> np.random.seed(10) # to reproduce these results >>> Z = np.random.normal(loc=0, scale=1, size=1000) >>> X = 2*Z + np.random.normal(loc=0, scale=1, size=1000) >>> Y = 3*X + 4*Z + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) Next, we will model cause-effect relationships as a probabilistic causal model and fit it to the data. >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('Z', 'Y'), ('Z', 'X'), ('X', 'Y')])) >>> causal_model.set_causal_mechanism('Z', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('X', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, data) Finally, we can estimate the strength of incoming arrows to a node of interest (e.g., :math:`Y`). >>> strength = gcm.arrow_strength(causal_model, 'Y') >>> strength {('X', 'Y'): 41.321925893102716, ('Z', 'Y'): 14.736197949517237} **Interpreting the results:** By default, the measurement unit of the scalar values for arrow strengths is variance for a continuous real-valued target, and the number of bits for a categorical target (i.e., KL divergence). Above, we observe that the direct influence from :math:`X` to :math:`Y` (~41.32) is stronger (by ~2.7 times) than the direct influence from :math:`Z` to :math:`Y` (~14.73). Roughly speaking, "removing" the arrow from :math:`X` to :math:`Y` increases the variance of :math:`Y` by ~41.32 units, whereas removing :math:`Z \to Y` increases the variance of :math:`Y` by ~14.73 units. In the next section, we explain what "removing" an edge implies. In particular, we briefly explain the science behind our method for quantifying the strength of an arrow. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ We will use the causal graph below to illustrate the key idea behind the method. .. image:: arrow_strength_example.png Here, we want to measure the strength of the arrow from node :math:`Z` to node :math:`Y`, while disregarding any indirect effects via :math:`X`. To achieve this, first recall that we can obtain the joint distribution of variables :math:`P` from their causal graph via a product of conditional distributions of each variable given its parents. We then create a new joint distribution :math:`P_{Z \to Y}` by cutting the edge from :math:`Z` to :math:`Y` and using an i.i.d. copy of :math:`Z` (denoted as :math:`Z'` in the figure) instead as input to :math:`Y`. The distribution of :math:`Z'` can be practically simulated by randomly shuffling the observed values of :math:`Z`. The strength of the arrow from :math:`Z` to :math:`Y`, represented as :math:`C_{Z \to Y}`, is then calculated as the distance between the post-cutting distribution:math:`P_{Z \to Y}` and the original joint distribution :math:`P`: .. math:: C_{Z \to Y} := D(P\; || P_{Z \to Y}) The distance metric :math:`D` utilized to calculate the arrow strength can be any suitable measure, such as the difference of variances or KL divergence. By default, the library uses a specific measure depending on the data type, but this can be fully customized to the use case. Note that when cutting the edge, only the causal mechanism of the target variable changes between the original and post-cutting joint distribution. As a result, any change in the marginal distribution of the target is due to the change in the causal mechanism of the target. This allows us to also quantify the arrow strength in terms of the change in the property (e.g., variance) of the marginal distribution of the target when we remove an edge. Customize the distance measure ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ By default, `arrow_strength` uses the difference of variances for measuring the arrow strength for a continuous real-valued target and employs KL divergence for measuring the arrow strength for a categorical target. But, we can also plug in our own choice of measure, using the ``difference_estimation_func`` parameter. For instance, to measure the arrow strength in terms of the change in the mean, we could define: >>> def mean_diff(Y_old, Y_new): return np.mean(Y_new) - np.mean(Y_old) and then estimate the arrow strength: >>> gcm.arrow_strength(causal_model, 'Y', difference_estimation_func=mean_diff) {('X', 'Y'): 0.11898914602350251, ('Z', 'Y'): 0.07811542095834415} These small results here are expected; in our example, the mean value of :math:`Y` remains :math:`0` regardless of whether we remove an incoming arrow. As such, the strength of incoming arrows to :math:`Y` with respect to their influence on the mean should be negligible. In summary, arrow strength can be measured in different units (e.g., mean, variance, bits). Therefore, we advise users to pick a meaningful unit---based on data and interpretation---to apply this method in practice.

bloebp

d7b7cc65c5b6780fbc0a32ec4cd9f94e17878353

7ca6de528ac70ec8cb2f29d2e0389149cec0090a

`the library` -> `DoWhy`

petergtz

py-why/dowhy

Revise arrow strength user guide

Signed-off-by: Patrick Bloebaum <bloebp@amazon.com>

2023-02-13 21:29:38+00:00

2023-03-07 16:14:39+00:00

docs/source/user_guide/gcm_based_inference/answering_causal_questions/quantify_arrow_strength.rst

Quantifying Arrow Strength ================================= By quantifying the strength of an arrow, we answer the question: How strong is the causal influence from a cause to its direct effect? How to use it ^^^^^^^^^^^^^^ To see how the method works, let us generate some data. >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> np.random.seed(10) # to reproduce these results >>> Z = np.random.normal(loc=0, scale=1, size=1000) >>> X = 2*Z + np.random.normal(loc=0, scale=1, size=1000) >>> Y = 3*X + 4*Z + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) Next, we will model cause-effect relationships as a probabilistic causal model and fit it to the data. >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('Z', 'Y'), ('Z', 'X'), ('X', 'Y')])) >>> causal_model.set_causal_mechanism('Z', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('X', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, data) Finally, we can estimate the strength of incoming arrows to a node of interest (e.g., :math:`Y`). >>> strength = gcm.arrow_strength(causal_model, 'Y') >>> strength {('X', 'Y'): 41.321925893102716, ('Z', 'Y'): 14.736197949517237} **Interpreting the results:** By default, the measurement unit of the scalar values for arrow strengths is variance for a continuous real-valued target, and the number of bits for a categorical target. Above, we observe that the direct influence from :math:`X` to :math:`Y` (~41.32) is stronger (by ~2.7 times) than the direct influence from :math:`Z` to :math:`Y` (~14.73). Roughly speaking, "removing" the arrow from :math:`X` to :math:`Y` increases the variance of :math:`Y` by ~41.32 units, whereas removing :math:`Z \to Y` increases the variance of :math:`Y` by ~14.73 units. In the next section, we explain what "removing" an edge implies. In particular, we briefly explain the science behind our method for quantifying the strength of an arrow. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ We will use the causal graph below to illustrate the key idea behind our method. .. image:: arrow_strength_example.png Recall that we can obtain the joint distribution of variables :math:`P` from their causal graph via a product of conditional distributions of each variable given its parents. To quantify the strength of an arrow from :math:`Z` to :math:`Y`, we define a new joint distribution :math:`P_{Z \to Y}`, also called post-cutting distribution, obtained by removing the edge :math:`Z \to Y`, and then feeding :math:`Y` with an i.i.d. copy of :math:`Z`. The i.i.d. copy can be simulated, in practice, by applying random permutation to samples of :math:`Z`. The strength of an arrow from :math:`Z` to :math:`Y`, denoted :math:`C_{Z \to Y}`, is then the distance (e.g., KL divergence) between the post-cutting distribution :math:`P_{Z \to Y}` and the original joint distribution :math:`P`. .. math:: C_{Z \to Y} := D_{\mathrm{KL}}(P\; || P_{Z \to Y}) Note that only the causal mechanism of the target variable (:math:`P_{Y \mid X, Z}` in the above example) changes between the original and the post-cutting joint distribution. Therefore, any change in the marginal distribution of the target (obtained by marginalising the joint distribution) is due to the change in the causal mechanism of the target variable. This means, we can also quantify the arrow strength in terms of the change in the property of the marginal distribution (e.g. mean, variance) of the target when we remove an edge. Measuring arrow strengths in different units ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ By default, `arrow_strength` employs KL divergence for measuring the arrow strength for categorical target, and difference in variance for continuous real-valued target. But we can also plug in our choice of measure, using the ``difference_estimation_func`` parameter. To measure the arrow strength in terms of the change in the mean, we could define: >>> def mean_diff(Y_old, Y_new): return np.mean(Y_new) - np.mean(Y_old) and then estimate the arrow strength: >>> gcm.arrow_strength(causal_model, 'Y', difference_estimation_func=mean_diff) {('X', 'Y'): 0.11898914602350251, ('Z', 'Y'): 0.07811542095834415} This is expected; in our example, the mean value of :math:`Y` remains :math:`0` regardless of whether we remove an incoming arrow. As such, the strength of incoming arrows to :math:`Y` should be negligible. In summary, arrow strength can be measured in different units (e.g., mean, variance, bits). Therefore, we advise users to pick a meaningful unit---based on data and interpretation---to apply this method in practice.

Quantifying Arrow Strength ================================= By quantifying the strength of an arrow, we answer the question: **How strong is the causal influence from a cause to its direct effect?** While there are different definitions for measuring causal influences in the literature, DoWhy offers an implementation for measuring the *direct* influence of a parent node on a child, where influences through paths over other nodes are ignored. This method is based on the paper: Dominik Janzing, David Balduzzi, Moritz Grosse-Wentrup, Bernhard Schölkopf. `Quantifying causal influences <https://www.jstor.org/stable/23566552>`_ The Annals of Statistics, Vol. 41, No. 5, 2324-2358, 2013. How to use it ^^^^^^^^^^^^^^ To see how to use the method, let us generate some data. >>> import numpy as np, pandas as pd, networkx as nx >>> from dowhy import gcm >>> np.random.seed(10) # to reproduce these results >>> Z = np.random.normal(loc=0, scale=1, size=1000) >>> X = 2*Z + np.random.normal(loc=0, scale=1, size=1000) >>> Y = 3*X + 4*Z + np.random.normal(loc=0, scale=1, size=1000) >>> data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) Next, we will model cause-effect relationships as a probabilistic causal model and fit it to the data. >>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('Z', 'Y'), ('Z', 'X'), ('X', 'Y')])) >>> causal_model.set_causal_mechanism('Z', gcm.EmpiricalDistribution()) >>> causal_model.set_causal_mechanism('X', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> causal_model.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) >>> gcm.fit(causal_model, data) Finally, we can estimate the strength of incoming arrows to a node of interest (e.g., :math:`Y`). >>> strength = gcm.arrow_strength(causal_model, 'Y') >>> strength {('X', 'Y'): 41.321925893102716, ('Z', 'Y'): 14.736197949517237} **Interpreting the results:** By default, the measurement unit of the scalar values for arrow strengths is variance for a continuous real-valued target, and the number of bits for a categorical target (i.e., KL divergence). Above, we observe that the direct influence from :math:`X` to :math:`Y` (~41.32) is stronger (by ~2.7 times) than the direct influence from :math:`Z` to :math:`Y` (~14.73). Roughly speaking, "removing" the arrow from :math:`X` to :math:`Y` increases the variance of :math:`Y` by ~41.32 units, whereas removing :math:`Z \to Y` increases the variance of :math:`Y` by ~14.73 units. In the next section, we explain what "removing" an edge implies. In particular, we briefly explain the science behind our method for quantifying the strength of an arrow. Understanding the method ^^^^^^^^^^^^^^^^^^^^^^^^ We will use the causal graph below to illustrate the key idea behind the method. .. image:: arrow_strength_example.png Here, we want to measure the strength of the arrow from node :math:`Z` to node :math:`Y`, while disregarding any indirect effects via :math:`X`. To achieve this, first recall that we can obtain the joint distribution of variables :math:`P` from their causal graph via a product of conditional distributions of each variable given its parents. We then create a new joint distribution :math:`P_{Z \to Y}` by cutting the edge from :math:`Z` to :math:`Y` and using an i.i.d. copy of :math:`Z` (denoted as :math:`Z'` in the figure) instead as input to :math:`Y`. The distribution of :math:`Z'` can be practically simulated by randomly shuffling the observed values of :math:`Z`. The strength of the arrow from :math:`Z` to :math:`Y`, represented as :math:`C_{Z \to Y}`, is then calculated as the distance between the post-cutting distribution:math:`P_{Z \to Y}` and the original joint distribution :math:`P`: .. math:: C_{Z \to Y} := D(P\; || P_{Z \to Y}) The distance metric :math:`D` utilized to calculate the arrow strength can be any suitable measure, such as the difference of variances or KL divergence. By default, the library uses a specific measure depending on the data type, but this can be fully customized to the use case. Note that when cutting the edge, only the causal mechanism of the target variable changes between the original and post-cutting joint distribution. As a result, any change in the marginal distribution of the target is due to the change in the causal mechanism of the target. This allows us to also quantify the arrow strength in terms of the change in the property (e.g., variance) of the marginal distribution of the target when we remove an edge. Customize the distance measure ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ By default, `arrow_strength` uses the difference of variances for measuring the arrow strength for a continuous real-valued target and employs KL divergence for measuring the arrow strength for a categorical target. But, we can also plug in our own choice of measure, using the ``difference_estimation_func`` parameter. For instance, to measure the arrow strength in terms of the change in the mean, we could define: >>> def mean_diff(Y_old, Y_new): return np.mean(Y_new) - np.mean(Y_old) and then estimate the arrow strength: >>> gcm.arrow_strength(causal_model, 'Y', difference_estimation_func=mean_diff) {('X', 'Y'): 0.11898914602350251, ('Z', 'Y'): 0.07811542095834415} These small results here are expected; in our example, the mean value of :math:`Y` remains :math:`0` regardless of whether we remove an incoming arrow. As such, the strength of incoming arrows to :math:`Y` with respect to their influence on the mean should be negligible. In summary, arrow strength can be measured in different units (e.g., mean, variance, bits). Therefore, we advise users to pick a meaningful unit---based on data and interpretation---to apply this method in practice.

bloebp

d7b7cc65c5b6780fbc0a32ec4cd9f94e17878353

7ca6de528ac70ec8cb2f29d2e0389149cec0090a

Nit: I would leave out "as mentioned before".

kailashbuki

py-why/dowhy

Enhancement: warn about unobserved graph variables in `causal_model.identify_effect`.

Closes #810. Introduces a `UserWarning` that is emitted if there are any graph variables that are not contained in the observed data (`self._data`). Adds a unit test for this implementation. Currently, the return values of `self.get_common_causes()`, `self.get_instruments()` and `self.get_effect_modifiers()` are considered as graph variables. In issue thread #810 there is also a suggestion to point out potential misspellings, for which I'd be happy to amend additional logic. See the questions in the last bullet point below to clarify the implementation in case we wish to add this. Design considerations and questions to reviewers: * Should we emit this via `self.logger.warning` instead? In my opinion, this will frequently point out improper usage (e.g., a typo in the columns of `self._data`) and hiding it in logging output that is not visible by default may not be desirable. But I'm open to suggestions. * Should this consider any other definition of *graph variables* than the one given above? * On handling misspellings (e.g., graph variable "AGE" vs data variable "AEG"): this would ideally use Levenshtein distance (e.g., with edit distance 1) to determine candidates. There are two options: using an external library (e.g., https://github.com/maxbachmann/Levenshtein) or a helper function. Which option is preferable? In case of a helper function, where would we best define it? Many thanks in advance for your help in pushing this feature across the finish line :) Best, MFreidank

2023-02-04 14:44:46+00:00

2023-02-14 20:21:29+00:00

dowhy/causal_model.py

""" Module containing the main model class for the dowhy package. """ import logging from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res

""" Module containing the main model class for the dowhy package. """ import logging import typing import warnings from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() # Emit a `UserWarning` if there are any unobserved graph variables and # and log a message highlighting data variables that are not part of the graph. graph_variable_names = set(self._graph.get_all_nodes(include_unobserved=True)) data_variable_names = set(self._data.columns) _warn_if_unobserved_graph_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) _warn_if_unused_data_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res def _warn_if_unobserved_graph_variables( graph_variable_names: typing.Set[str], data_variable_names: typing.Set[str], logger: logging.Logger, ): """Emits a warning if there are any graph variables that are not observed in the data.""" unobserved_graph_variable_names = graph_variable_names.difference(data_variable_names) if unobserved_graph_variable_names: observed_graph_variable_names = graph_variable_names.intersection(data_variable_names) num_graph_variables = len(graph_variable_names) num_unobserved_graph_variables = len(unobserved_graph_variable_names) num_observed_graph_variables = len(observed_graph_variable_names) warnings.warn( f"{num_unobserved_graph_variables} variables are assumed " "unobserved because they are not in the dataset. " "Configure the logging level to `logging.WARNING` or higher for additional details." ) logger.warn( "The graph defines %d variables. %d were found in the dataset " "and will be analyzed as observed variables. %d were not found " "in the dataset and will be analyzed as unobserved variables. " "The observed variables are: '%s'. " "The unobserved variables are: '%s'. " "If this matches your expectations for observations, please continue. " "If you expected any of the unobserved variables to be in the " "dataframe, please check for typos.", num_graph_variables, num_observed_graph_variables, num_unobserved_graph_variables, sorted(observed_graph_variable_names), sorted(unobserved_graph_variable_names), ) def _warn_if_unused_data_variables( data_variable_names: typing.Set[str], graph_variable_names: typing.Set[str], logger: logging.Logger, ): """Logs a warning message if there are any data variables that are not used in the graph.""" unused_data_variable_names = data_variable_names.difference(graph_variable_names) if unused_data_variable_names: logger.warn( "There are an additional %d variables in the dataset that are " "not in the graph. Variable names are: '%s'", len(unused_data_variable_names), sorted(unused_data_variable_names), )

MFreidank

2a2b3f4f7d02f8157d4b2ea39588b305e048eca8

23214a9850544780e21f0afecb390446ceca48a2

From the wording, it's not clear whether this is an ok or not ok thing. To resolve this, I'd suggest giving a little more guidance. For larger graphs, we might also want to add counts too. Maybe something like: "The graph defines N variables. K were found in the dataset and will be analyzed as observed variables. N-K were not found in the dataset and will be analyzed as unobserved variables. The observed variables are: ... The unobserved variables are ... If this matches your expectations for observations, please continue. If you expected any of these unobserved variables to be in the dataframe, please check for typos." Maybe also "there are an additional Z variables in the dataset that are not in the graph".

emrekiciman

py-why/dowhy

Enhancement: warn about unobserved graph variables in `causal_model.identify_effect`.

Closes #810. Introduces a `UserWarning` that is emitted if there are any graph variables that are not contained in the observed data (`self._data`). Adds a unit test for this implementation. Currently, the return values of `self.get_common_causes()`, `self.get_instruments()` and `self.get_effect_modifiers()` are considered as graph variables. In issue thread #810 there is also a suggestion to point out potential misspellings, for which I'd be happy to amend additional logic. See the questions in the last bullet point below to clarify the implementation in case we wish to add this. Design considerations and questions to reviewers: * Should we emit this via `self.logger.warning` instead? In my opinion, this will frequently point out improper usage (e.g., a typo in the columns of `self._data`) and hiding it in logging output that is not visible by default may not be desirable. But I'm open to suggestions. * Should this consider any other definition of *graph variables* than the one given above? * On handling misspellings (e.g., graph variable "AGE" vs data variable "AEG"): this would ideally use Levenshtein distance (e.g., with edit distance 1) to determine candidates. There are two options: using an external library (e.g., https://github.com/maxbachmann/Levenshtein) or a helper function. Which option is preferable? In case of a helper function, where would we best define it? Many thanks in advance for your help in pushing this feature across the finish line :) Best, MFreidank

2023-02-04 14:44:46+00:00

2023-02-14 20:21:29+00:00

dowhy/causal_model.py

""" Module containing the main model class for the dowhy package. """ import logging from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res

""" Module containing the main model class for the dowhy package. """ import logging import typing import warnings from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() # Emit a `UserWarning` if there are any unobserved graph variables and # and log a message highlighting data variables that are not part of the graph. graph_variable_names = set(self._graph.get_all_nodes(include_unobserved=True)) data_variable_names = set(self._data.columns) _warn_if_unobserved_graph_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) _warn_if_unused_data_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res def _warn_if_unobserved_graph_variables( graph_variable_names: typing.Set[str], data_variable_names: typing.Set[str], logger: logging.Logger, ): """Emits a warning if there are any graph variables that are not observed in the data.""" unobserved_graph_variable_names = graph_variable_names.difference(data_variable_names) if unobserved_graph_variable_names: observed_graph_variable_names = graph_variable_names.intersection(data_variable_names) num_graph_variables = len(graph_variable_names) num_unobserved_graph_variables = len(unobserved_graph_variable_names) num_observed_graph_variables = len(observed_graph_variable_names) warnings.warn( f"{num_unobserved_graph_variables} variables are assumed " "unobserved because they are not in the dataset. " "Configure the logging level to `logging.WARNING` or higher for additional details." ) logger.warn( "The graph defines %d variables. %d were found in the dataset " "and will be analyzed as observed variables. %d were not found " "in the dataset and will be analyzed as unobserved variables. " "The observed variables are: '%s'. " "The unobserved variables are: '%s'. " "If this matches your expectations for observations, please continue. " "If you expected any of the unobserved variables to be in the " "dataframe, please check for typos.", num_graph_variables, num_observed_graph_variables, num_unobserved_graph_variables, sorted(observed_graph_variable_names), sorted(unobserved_graph_variable_names), ) def _warn_if_unused_data_variables( data_variable_names: typing.Set[str], graph_variable_names: typing.Set[str], logger: logging.Logger, ): """Logs a warning message if there are any data variables that are not used in the graph.""" unused_data_variable_names = data_variable_names.difference(graph_variable_names) if unused_data_variable_names: logger.warn( "There are an additional %d variables in the dataset that are " "not in the graph. Variable names are: '%s'", len(unused_data_variable_names), sorted(unused_data_variable_names), )

MFreidank

2a2b3f4f7d02f8157d4b2ea39588b305e048eca8

23214a9850544780e21f0afecb390446ceca48a2

I think you could check all variables by calling causalgraph.py CausalGraph::get_all_nodes(...)

emrekiciman

py-why/dowhy

Enhancement: warn about unobserved graph variables in `causal_model.identify_effect`.

Closes #810. Introduces a `UserWarning` that is emitted if there are any graph variables that are not contained in the observed data (`self._data`). Adds a unit test for this implementation. Currently, the return values of `self.get_common_causes()`, `self.get_instruments()` and `self.get_effect_modifiers()` are considered as graph variables. In issue thread #810 there is also a suggestion to point out potential misspellings, for which I'd be happy to amend additional logic. See the questions in the last bullet point below to clarify the implementation in case we wish to add this. Design considerations and questions to reviewers: * Should we emit this via `self.logger.warning` instead? In my opinion, this will frequently point out improper usage (e.g., a typo in the columns of `self._data`) and hiding it in logging output that is not visible by default may not be desirable. But I'm open to suggestions. * Should this consider any other definition of *graph variables* than the one given above? * On handling misspellings (e.g., graph variable "AGE" vs data variable "AEG"): this would ideally use Levenshtein distance (e.g., with edit distance 1) to determine candidates. There are two options: using an external library (e.g., https://github.com/maxbachmann/Levenshtein) or a helper function. Which option is preferable? In case of a helper function, where would we best define it? Many thanks in advance for your help in pushing this feature across the finish line :) Best, MFreidank

2023-02-04 14:44:46+00:00

2023-02-14 20:21:29+00:00

dowhy/causal_model.py

""" Module containing the main model class for the dowhy package. """ import logging from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res

""" Module containing the main model class for the dowhy package. """ import logging import typing import warnings from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() # Emit a `UserWarning` if there are any unobserved graph variables and # and log a message highlighting data variables that are not part of the graph. graph_variable_names = set(self._graph.get_all_nodes(include_unobserved=True)) data_variable_names = set(self._data.columns) _warn_if_unobserved_graph_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) _warn_if_unused_data_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res def _warn_if_unobserved_graph_variables( graph_variable_names: typing.Set[str], data_variable_names: typing.Set[str], logger: logging.Logger, ): """Emits a warning if there are any graph variables that are not observed in the data.""" unobserved_graph_variable_names = graph_variable_names.difference(data_variable_names) if unobserved_graph_variable_names: observed_graph_variable_names = graph_variable_names.intersection(data_variable_names) num_graph_variables = len(graph_variable_names) num_unobserved_graph_variables = len(unobserved_graph_variable_names) num_observed_graph_variables = len(observed_graph_variable_names) warnings.warn( f"{num_unobserved_graph_variables} variables are assumed " "unobserved because they are not in the dataset. " "Configure the logging level to `logging.WARNING` or higher for additional details." ) logger.warn( "The graph defines %d variables. %d were found in the dataset " "and will be analyzed as observed variables. %d were not found " "in the dataset and will be analyzed as unobserved variables. " "The observed variables are: '%s'. " "The unobserved variables are: '%s'. " "If this matches your expectations for observations, please continue. " "If you expected any of the unobserved variables to be in the " "dataframe, please check for typos.", num_graph_variables, num_observed_graph_variables, num_unobserved_graph_variables, sorted(observed_graph_variable_names), sorted(unobserved_graph_variable_names), ) def _warn_if_unused_data_variables( data_variable_names: typing.Set[str], graph_variable_names: typing.Set[str], logger: logging.Logger, ): """Logs a warning message if there are any data variables that are not used in the graph.""" unused_data_variable_names = data_variable_names.difference(graph_variable_names) if unused_data_variable_names: logger.warn( "There are an additional %d variables in the dataset that are " "not in the graph. Variable names are: '%s'", len(unused_data_variable_names), sorted(unused_data_variable_names), )

MFreidank

2a2b3f4f7d02f8157d4b2ea39588b305e048eca8

23214a9850544780e21f0afecb390446ceca48a2

Regarding your comment about whether the warnings should be visible or not by default ... how about we have a short message that says "N variables are assumed unobserved because they are not in the dataset. Pass/set the ____ flag for additional details".

emrekiciman

py-why/dowhy

Enhancement: warn about unobserved graph variables in `causal_model.identify_effect`.

Closes #810. Introduces a `UserWarning` that is emitted if there are any graph variables that are not contained in the observed data (`self._data`). Adds a unit test for this implementation. Currently, the return values of `self.get_common_causes()`, `self.get_instruments()` and `self.get_effect_modifiers()` are considered as graph variables. In issue thread #810 there is also a suggestion to point out potential misspellings, for which I'd be happy to amend additional logic. See the questions in the last bullet point below to clarify the implementation in case we wish to add this. Design considerations and questions to reviewers: * Should we emit this via `self.logger.warning` instead? In my opinion, this will frequently point out improper usage (e.g., a typo in the columns of `self._data`) and hiding it in logging output that is not visible by default may not be desirable. But I'm open to suggestions. * Should this consider any other definition of *graph variables* than the one given above? * On handling misspellings (e.g., graph variable "AGE" vs data variable "AEG"): this would ideally use Levenshtein distance (e.g., with edit distance 1) to determine candidates. There are two options: using an external library (e.g., https://github.com/maxbachmann/Levenshtein) or a helper function. Which option is preferable? In case of a helper function, where would we best define it? Many thanks in advance for your help in pushing this feature across the finish line :) Best, MFreidank

2023-02-04 14:44:46+00:00

2023-02-14 20:21:29+00:00

dowhy/causal_model.py

""" Module containing the main model class for the dowhy package. """ import logging from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res

""" Module containing the main model class for the dowhy package. """ import logging import typing import warnings from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() # Emit a `UserWarning` if there are any unobserved graph variables and # and log a message highlighting data variables that are not part of the graph. graph_variable_names = set(self._graph.get_all_nodes(include_unobserved=True)) data_variable_names = set(self._data.columns) _warn_if_unobserved_graph_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) _warn_if_unused_data_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res def _warn_if_unobserved_graph_variables( graph_variable_names: typing.Set[str], data_variable_names: typing.Set[str], logger: logging.Logger, ): """Emits a warning if there are any graph variables that are not observed in the data.""" unobserved_graph_variable_names = graph_variable_names.difference(data_variable_names) if unobserved_graph_variable_names: observed_graph_variable_names = graph_variable_names.intersection(data_variable_names) num_graph_variables = len(graph_variable_names) num_unobserved_graph_variables = len(unobserved_graph_variable_names) num_observed_graph_variables = len(observed_graph_variable_names) warnings.warn( f"{num_unobserved_graph_variables} variables are assumed " "unobserved because they are not in the dataset. " "Configure the logging level to `logging.WARNING` or higher for additional details." ) logger.warn( "The graph defines %d variables. %d were found in the dataset " "and will be analyzed as observed variables. %d were not found " "in the dataset and will be analyzed as unobserved variables. " "The observed variables are: '%s'. " "The unobserved variables are: '%s'. " "If this matches your expectations for observations, please continue. " "If you expected any of the unobserved variables to be in the " "dataframe, please check for typos.", num_graph_variables, num_observed_graph_variables, num_unobserved_graph_variables, sorted(observed_graph_variable_names), sorted(unobserved_graph_variable_names), ) def _warn_if_unused_data_variables( data_variable_names: typing.Set[str], graph_variable_names: typing.Set[str], logger: logging.Logger, ): """Logs a warning message if there are any data variables that are not used in the graph.""" unused_data_variable_names = data_variable_names.difference(graph_variable_names) if unused_data_variable_names: logger.warn( "There are an additional %d variables in the dataset that are " "not in the graph. Variable names are: '%s'", len(unused_data_variable_names), sorted(unused_data_variable_names), )

MFreidank

2a2b3f4f7d02f8157d4b2ea39588b305e048eca8

23214a9850544780e21f0afecb390446ceca48a2

I've tried to adapt the logging to resolve your comments. There are now two levels to the output: * A high level warning, emitted using `warnings.warn` that points out the issue and suggests additional details are available when configuring `logging` levels. * A lower level, more detailed warning, emitted using `self.logger.warn` that follows the format you describe above. Regarding your last point *there are an additional Z variables in the dataset that are not in the graph*, I decided to treat this under a separate conditional (as it may occur in cases without unobserved graph variables). This seems to me like it may be less likely to unveil a user issue and will only be visible when `logging` is configured to at least the `WARNING` level. Let me know your thoughts and if this seems ready for you.

MFreidank

py-why/dowhy

Enhancement: warn about unobserved graph variables in `causal_model.identify_effect`.

Closes #810. Introduces a `UserWarning` that is emitted if there are any graph variables that are not contained in the observed data (`self._data`). Adds a unit test for this implementation. Currently, the return values of `self.get_common_causes()`, `self.get_instruments()` and `self.get_effect_modifiers()` are considered as graph variables. In issue thread #810 there is also a suggestion to point out potential misspellings, for which I'd be happy to amend additional logic. See the questions in the last bullet point below to clarify the implementation in case we wish to add this. Design considerations and questions to reviewers: * Should we emit this via `self.logger.warning` instead? In my opinion, this will frequently point out improper usage (e.g., a typo in the columns of `self._data`) and hiding it in logging output that is not visible by default may not be desirable. But I'm open to suggestions. * Should this consider any other definition of *graph variables* than the one given above? * On handling misspellings (e.g., graph variable "AGE" vs data variable "AEG"): this would ideally use Levenshtein distance (e.g., with edit distance 1) to determine candidates. There are two options: using an external library (e.g., https://github.com/maxbachmann/Levenshtein) or a helper function. Which option is preferable? In case of a helper function, where would we best define it? Many thanks in advance for your help in pushing this feature across the finish line :) Best, MFreidank

2023-02-04 14:44:46+00:00

2023-02-14 20:21:29+00:00

dowhy/causal_model.py

""" Module containing the main model class for the dowhy package. """ import logging from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res

""" Module containing the main model class for the dowhy package. """ import logging import typing import warnings from itertools import combinations from sympy import init_printing import dowhy.causal_estimators as causal_estimators import dowhy.causal_refuters as causal_refuters import dowhy.graph_learners as graph_learners import dowhy.utils.cli_helpers as cli from dowhy.causal_estimator import CausalEstimate, estimate_effect from dowhy.causal_graph import CausalGraph from dowhy.causal_identifier import AutoIdentifier, BackdoorAdjustment, IDIdentifier from dowhy.causal_identifier.identify_effect import EstimandType from dowhy.causal_refuters.graph_refuter import GraphRefuter from dowhy.utils.api import parse_state init_printing() # To display symbolic math symbols class CausalModel: """Main class for storing the causal model state.""" def __init__( self, data, treatment, outcome, graph=None, common_causes=None, instruments=None, effect_modifiers=None, estimand_type="nonparametric-ate", proceed_when_unidentifiable=False, missing_nodes_as_confounders=False, identify_vars=False, **kwargs, ): """Initialize data and create a causal graph instance. Assigns treatment and outcome variables. Also checks and finds the common causes and instruments for treatment and outcome. At least one of graph, common_causes or instruments must be provided. If none of these variables are provided, then learn_graph() can be used later. :param data: a pandas dataframe containing treatment, outcome and other variables. :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param graph: path to DOT file containing a DAG or a string containing a DAG specification in DOT format :param common_causes: names of common causes of treatment and _outcome. Only used when graph is None. :param instruments: names of instrumental variables for the effect of treatment on outcome. Only used when graph is None. :param effect_modifiers: names of variables that can modify the treatment effect. If not provided, then the causal graph is used to find the effect modifiers. Estimators will return multiple different estimates based on each value of effect_modifiers. :param estimand_type: the type of estimand requested (currently only "nonparametric-ate" is supported). In the future, may support other specific parametric forms of identification. :param proceed_when_unidentifiable: does the identification proceed by ignoring potential unobserved confounders. Binary flag. :param missing_nodes_as_confounders: Binary flag indicating whether variables in the dataframe that are not included in the causal graph, should be automatically included as confounder nodes. :param identify_vars: Variable deciding whether to compute common causes, instruments and effect modifiers while initializing the class. identify_vars should be set to False when user is providing common_causes, instruments or effect modifiers on their own(otherwise the identify_vars code can override the user provided values). Also it does not make sense if no graph is given. :returns: an instance of CausalModel class """ self._data = data self._treatment = parse_state(treatment) self._outcome = parse_state(outcome) self._effect_modifiers = parse_state(effect_modifiers) self._estimand_type = estimand_type self._proceed_when_unidentifiable = proceed_when_unidentifiable self._missing_nodes_as_confounders = missing_nodes_as_confounders self.logger = logging.getLogger(__name__) self._estimator_cache = {} if graph is None: self.logger.warning("Causal Graph not provided. DoWhy will construct a graph based on data inputs.") self._common_causes = parse_state(common_causes) self._instruments = parse_state(instruments) if common_causes is not None and instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif common_causes is not None: self._graph = CausalGraph( self._treatment, self._outcome, common_cause_names=self._common_causes, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) elif instruments is not None: self._graph = CausalGraph( self._treatment, self._outcome, instrument_names=self._instruments, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.logger.warning( "Relevant variables to build causal graph not provided. You may want to use the learn_graph() function to construct the causal graph." ) self._graph = CausalGraph( self._treatment, self._outcome, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), ) else: self.init_graph(graph=graph, identify_vars=identify_vars) self._other_variables = kwargs self.summary() # Emit a `UserWarning` if there are any unobserved graph variables and # and log a message highlighting data variables that are not part of the graph. graph_variable_names = set(self._graph.get_all_nodes(include_unobserved=True)) data_variable_names = set(self._data.columns) _warn_if_unobserved_graph_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) _warn_if_unused_data_variables( graph_variable_names=graph_variable_names, data_variable_names=data_variable_names, logger=self.logger, ) def init_graph(self, graph, identify_vars): """ Initialize self._graph using graph provided by the user. """ # Create causal graph object self._graph = CausalGraph( self._treatment, self._outcome, graph, effect_modifier_names=self._effect_modifiers, observed_node_names=self._data.columns.tolist(), missing_nodes_as_confounders=self._missing_nodes_as_confounders, ) if identify_vars: self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) self._instruments = self._graph.get_instruments(self._treatment, self._outcome) # Sometimes, effect modifiers from the graph may not match those provided by the user. # (Because some effect modifiers may also be common causes) # In such cases, the user-provided modifiers are used. # If no effect modifiers are provided, then the ones from the graph are used. if self._effect_modifiers is None or not self._effect_modifiers: self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) def get_common_causes(self): self._common_causes = self._graph.get_common_causes(self._treatment, self._outcome) return self._common_causes def get_instruments(self): self._instruments = self._graph.get_instruments(self._treatment, self._outcome) return self._instruments def get_effect_modifiers(self): self._effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) return self._effect_modifiers def learn_graph(self, method_name="cdt.causality.graph.LiNGAM", *args, **kwargs): """ Learn causal graph from the data. This function takes the method name as input and initializes the causal graph object using the learnt graph. :param self: instance of the CausalModel class (or its subclass) :param method_name: Exact method name of the object to be imported from the concerned library. :returns: an instance of the CausalGraph class initialized with the learned graph. """ # Import causal discovery class str_arr = method_name.split(".", maxsplit=1) library_name = str_arr[0] causal_discovery_class = graph_learners.get_discovery_class_object(library_name) model = causal_discovery_class(self._data, method_name, *args, **kwargs) graph = model.learn_graph() # Initialize causal graph object self.init_graph(graph=graph) return self._graph def identify_effect( self, estimand_type=None, method_name="default", proceed_when_unidentifiable=None, optimize_backdoor=False ): """Identify the causal effect to be estimated, using properties of the causal graph. :param method_name: Method name for identification algorithm. ("id-algorithm" or "default") :param proceed_when_unidentifiable: Binary flag indicating whether identification should proceed in the presence of (potential) unobserved confounders. :returns: a probability expression (estimand) for the causal effect if identified, else NULL """ if proceed_when_unidentifiable is None: proceed_when_unidentifiable = self._proceed_when_unidentifiable if estimand_type is None: estimand_type = self._estimand_type estimand_type = EstimandType(estimand_type) if method_name == "id-algorithm": identifier = IDIdentifier() else: identifier = AutoIdentifier( estimand_type=estimand_type, backdoor_adjustment=BackdoorAdjustment(method_name), proceed_when_unidentifiable=proceed_when_unidentifiable, optimize_backdoor=optimize_backdoor, ) identified_estimand = identifier.identify_effect( graph=self._graph, treatment_name=self._treatment, outcome_name=self._outcome ) self.identifier = identifier return identified_estimand def estimate_effect( self, identified_estimand, method_name=None, control_value=0, treatment_value=1, test_significance=None, evaluate_effect_strength=False, confidence_intervals=False, target_units="ate", effect_modifiers=None, fit_estimator=True, method_params=None, ): """Estimate the identified causal effect. Currently requires an explicit method name to be specified. Method names follow the convention of identification method followed by the specific estimation method: "[backdoor/iv].estimation_method_name". Following methods are supported. * Propensity Score Matching: "backdoor.propensity_score_matching" * Propensity Score Stratification: "backdoor.propensity_score_stratification" * Propensity Score-based Inverse Weighting: "backdoor.propensity_score_weighting" * Linear Regression: "backdoor.linear_regression" * Generalized Linear Models (e.g., logistic regression): "backdoor.generalized_linear_model" * Instrumental Variables: "iv.instrumental_variable" * Regression Discontinuity: "iv.regression_discontinuity" In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: name of the estimation method to be used. :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param test_significance: Binary flag on whether to additionally do a statistical signficance test for the estimate. :param evaluate_effect_strength: (Experimental) Binary flag on whether to estimate the relative strength of the treatment's effect. This measure can be used to compare different treatments for the same outcome (by running this method with different treatments sequentially). :param confidence_intervals: (Experimental) Binary flag indicating whether confidence intervals should be computed. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. See the docs for each estimation method for allowed method-specific params. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None or len(effect_modifiers) == 0: effect_modifiers = self._graph.get_effect_modifiers(self._treatment, self._outcome) if method_name is None: # TODO add propensity score as default backdoor method, iv as default iv method, add an informational message to show which method has been selected. pass else: # TODO add dowhy as a prefix to all dowhy estimators num_components = len(method_name.split(".")) str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] # This is done as all dowhy estimators have two parts and external ones have two or more parts if num_components > 2: estimator_package = estimator_name.split(".")[0] if estimator_package == "dowhy": # For updated dowhy methods estimator_method = estimator_name.split(".", maxsplit=1)[ 1 ] # discard dowhy from the full package name causal_estimator_class = causal_estimators.get_class_object(estimator_method + "_estimator") else: third_party_estimator_package = estimator_package causal_estimator_class = causal_estimators.get_class_object( third_party_estimator_package, estimator_name ) if method_params is None: method_params = {} # Define the third-party estimation method to be used method_params[third_party_estimator_package + "_estimator"] = estimator_name else: # For older dowhy methods self.logger.info(estimator_name) # Process the dowhy estimators causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") if method_params is not None and (num_components <= 2 or estimator_package == "dowhy"): extra_args = method_params.get("init_params", {}) else: extra_args = {} if method_params is None: method_params = {} identified_estimand.set_identifier_method(identifier_name) if not fit_estimator and method_name in self._estimator_cache: causal_estimator = self._estimator_cache[method_name] else: causal_estimator = causal_estimator_class( identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, **method_params, **extra_args, ) self._estimator_cache[method_name] = causal_estimator return estimate_effect( self._data, self._treatment, self._outcome, identifier_name, causal_estimator, control_value, treatment_value, target_units, effect_modifiers, fit_estimator, method_params, ) def do(self, x, identified_estimand, method_name=None, fit_estimator=True, method_params=None): """Do operator for estimating values of the outcome after intervening on treatment. :param x: interventional value of the treatment variable :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param method_name: any of the estimation method to be used. See docs for estimate_effect method for a list of supported estimation methods. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to compute the do-operation on new data using a previously fitted estimator. :param method_params: Dictionary containing any method-specific parameters. These are passed directly to the estimating method. :returns: an instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if method_name is None: pass else: str_arr = method_name.split(".", maxsplit=1) identifier_name = str_arr[0] estimator_name = str_arr[1] identified_estimand.set_identifier_method(identifier_name) causal_estimator_class = causal_estimators.get_class_object(estimator_name + "_estimator") # Check if estimator's target estimand is identified if identified_estimand.estimands[identifier_name] is None: self.logger.warning("No valid identified estimand for using instrumental variables method") estimate = CausalEstimate(None, None, None, None, None, None) else: if fit_estimator: # Note that while the name of the variable is the same, # "self.causal_estimator", this estimator takes in less # parameters than the same from the # estimate_effect code. It is not advisable to use the # estimator from this function to call estimate_effect # with fit_estimator=False. self.causal_estimator = causal_estimator_class( identified_estimand, **method_params, ) self.causal_estimator.fit( self._data, self._treatment, self._outcome, ) else: # Estimator had been computed in a previous call assert self.causal_estimator is not None try: estimate = self.causal_estimator.do(x) except NotImplementedError: self.logger.error("Do Operation not implemented or not supported for this estimator.") raise NotImplementedError return estimate def refute_estimate(self, estimand, estimate, method_name=None, show_progress_bar=False, **kwargs): """Refute an estimated causal effect. If method_name is provided, uses the provided method. In the future, we may support automatic selection of suitable refutation tests. Following refutation methods are supported. * Adding a randomly-generated confounder: "random_common_cause" * Adding a confounder that is associated with both treatment and outcome: "add_unobserved_common_cause" * Replacing the treatment with a placebo (random) variable): "placebo_treatment_refuter" * Removing a random subset of the data: "data_subset_refuter" :param estimand: target estimand, an instance of the IdentifiedEstimand class (typically, the output of identify_effect) :param estimate: estimate to be refuted, an instance of the CausalEstimate class (typically, the output of estimate_effect) :param method_name: name of the refutation method :param show_progress_bar: Boolean flag on whether to show a progress bar :param kwargs: (optional) additional arguments that are passed directly to the refutation method. Can specify a random seed here to ensure reproducible results ('random_seed' parameter). For method-specific parameters, consult the documentation for the specific method. All refutation methods are in the causal_refuters subpackage. :returns: an instance of the RefuteResult class """ if estimate is None or estimate.value is None: self.logger.error("Aborting refutation! No estimate is provided.") raise ValueError("Aborting refutation! No valid estimate is provided.") if method_name is None: pass else: refuter_class = causal_refuters.get_class_object(method_name) refuter = refuter_class(self._data, identified_estimand=estimand, estimate=estimate, **kwargs) res = refuter.refute_estimate(show_progress_bar) return res def view_model(self, layout="dot", size=(8, 6), file_name="causal_model"): """View the causal DAG. :param layout: string specifying the layout of the graph. :param size: tuple (x, y) specifying the width and height of the figure in inches. :param file_name: string specifying the file name for the saved causal graph png. :returns: a visualization of the graph """ self._graph.view_graph(layout, size, file_name) def interpret(self, method_name=None, **kwargs): """Interpret the causal model. :param method_name: method used for interpreting the model. If None, then default interpreter is chosen that describes the model summary and shows the associated causal graph. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: self.summary(print_to_stdout=True) self.view_model() return method_name_arr = parse_state(method_name) import dowhy.interpreters as interpreters for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def summary(self, print_to_stdout=False): """Print a text summary of the model. :returns: a string containining the summary """ summary_text = "Model to find the causal effect of treatment {0} on outcome {1}".format( self._treatment, self._outcome ) self.logger.info(summary_text) if print_to_stdout: print(summary_text) return summary_text def refute_graph(self, k=1, independence_test=None, independence_constraints=None): """ Check if the dependencies in input graph matches with the dataset - ( X ⫫ Y ) | Z where X and Y are considered as singleton sets currently Z can have multiple variables :param k: number of covariates in set Z :param independence_test: dictionary containing methods to test conditional independece in data :param independence_constraints: list of implications to be test input by the user in the format [(x,y,(z1,z2)), (x,y, (z3,)) ] : returns: an instance of GraphRefuter class """ if independence_test is not None: test_for_continuous = independence_test["test_for_continuous"] test_for_discrete = independence_test["test_for_discrete"] refuter = GraphRefuter( data=self._data, method_name_continuous=test_for_continuous, method_name_discrete=test_for_discrete ) else: refuter = GraphRefuter(data=self._data) if independence_constraints is None: all_nodes = list(self._graph.get_all_nodes(include_unobserved=False)) num_nodes = len(all_nodes) array_indices = list(range(0, num_nodes)) all_possible_combinations = list( combinations(array_indices, 2) ) # Generating sets of indices of size 2 for different x and y conditional_independences = [] self.logger.info("The followed conditional independences are true for the input graph") for combination in all_possible_combinations: # Iterate over the unique 2-sized sets [x,y] i = combination[0] j = combination[1] a = all_nodes[i] b = all_nodes[j] if i < j: temp_arr = all_nodes[:i] + all_nodes[i + 1 : j] + all_nodes[j + 1 :] else: temp_arr = all_nodes[:j] + all_nodes[j + 1 : i] + all_nodes[i + 1 :] k_sized_lists = list(combinations(temp_arr, k)) for k_list in k_sized_lists: if self._graph.check_dseparation([str(a)], [str(b)], k_list) == True: self.logger.info(" %s and %s are CI given %s ", a, b, k_list) conditional_independences.append([a, b, k_list]) independence_constraints = conditional_independences res = refuter.refute_model(independence_constraints=independence_constraints) self.logger.info(refuter._refutation_passed) return res def _warn_if_unobserved_graph_variables( graph_variable_names: typing.Set[str], data_variable_names: typing.Set[str], logger: logging.Logger, ): """Emits a warning if there are any graph variables that are not observed in the data.""" unobserved_graph_variable_names = graph_variable_names.difference(data_variable_names) if unobserved_graph_variable_names: observed_graph_variable_names = graph_variable_names.intersection(data_variable_names) num_graph_variables = len(graph_variable_names) num_unobserved_graph_variables = len(unobserved_graph_variable_names) num_observed_graph_variables = len(observed_graph_variable_names) warnings.warn( f"{num_unobserved_graph_variables} variables are assumed " "unobserved because they are not in the dataset. " "Configure the logging level to `logging.WARNING` or higher for additional details." ) logger.warn( "The graph defines %d variables. %d were found in the dataset " "and will be analyzed as observed variables. %d were not found " "in the dataset and will be analyzed as unobserved variables. " "The observed variables are: '%s'. " "The unobserved variables are: '%s'. " "If this matches your expectations for observations, please continue. " "If you expected any of the unobserved variables to be in the " "dataframe, please check for typos.", num_graph_variables, num_observed_graph_variables, num_unobserved_graph_variables, sorted(observed_graph_variable_names), sorted(unobserved_graph_variable_names), ) def _warn_if_unused_data_variables( data_variable_names: typing.Set[str], graph_variable_names: typing.Set[str], logger: logging.Logger, ): """Logs a warning message if there are any data variables that are not used in the graph.""" unused_data_variable_names = data_variable_names.difference(graph_variable_names) if unused_data_variable_names: logger.warn( "There are an additional %d variables in the dataset that are " "not in the graph. Variable names are: '%s'", len(unused_data_variable_names), sorted(unused_data_variable_names), )

MFreidank

2a2b3f4f7d02f8157d4b2ea39588b305e048eca8

23214a9850544780e21f0afecb390446ceca48a2

That's easier indeed, thanks for pointing this out. Resolved now.

MFreidank

py-why/dowhy

Enhancement: warn about unobserved graph variables in `causal_model.identify_effect`.

Closes #810. Introduces a `UserWarning` that is emitted if there are any graph variables that are not contained in the observed data (`self._data`). Adds a unit test for this implementation. Currently, the return values of `self.get_common_causes()`, `self.get_instruments()` and `self.get_effect_modifiers()` are considered as graph variables. In issue thread #810 there is also a suggestion to point out potential misspellings, for which I'd be happy to amend additional logic. See the questions in the last bullet point below to clarify the implementation in case we wish to add this. Design considerations and questions to reviewers: * Should we emit this via `self.logger.warning` instead? In my opinion, this will frequently point out improper usage (e.g., a typo in the columns of `self._data`) and hiding it in logging output that is not visible by default may not be desirable. But I'm open to suggestions. * Should this consider any other definition of *graph variables* than the one given above? * On handling misspellings (e.g., graph variable "AGE" vs data variable "AEG"): this would ideally use Levenshtein distance (e.g., with edit distance 1) to determine candidates. There are two options: using an external library (e.g., https://github.com/maxbachmann/Levenshtein) or a helper function. Which option is preferable? In case of a helper function, where would we best define it? Many thanks in advance for your help in pushing this feature across the finish line :) Best, MFreidank

2023-02-04 14:44:46+00:00

2023-02-14 20:21:29+00:00

tests/test_causal_model.py

import pandas as pd import pytest from pytest import mark from sklearn import linear_model import dowhy import dowhy.datasets from dowhy import CausalModel class TestCausalModel(object): @mark.parametrize( ["beta", "num_samples", "num_treatments"], [ (10, 100, 1), ], ) def test_external_estimator(self, beta, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) estimate = model.estimate_effect( identified_estimand, method_name="backdoor.tests.causal_estimators.mock_external_estimator.PropensityScoreWeightingEstimator", control_value=0, treatment_value=1, target_units="ate", # condition used for CATE confidence_intervals=True, method_params={"propensity_score_model": linear_model.LogisticRegression(max_iter=1000)}, ) assert estimate.estimator.propensity_score_model.max_iter == 1000 @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = 'graph[directed 1 node[ id "{0}" label "{0}"]node[ id "{1}" label "{1}"]node[ id "Unobserved Confounders" label "Unobserved Confounders"]edge[source "{0}" target "{1}"]edge[source "Unobserved Confounders" target "{0}"]edge[source "Unobserved Confounders" target "{1}"]node[ id "X0" label "X0"] edge[ source "X0" target "{0}"] node[ id "X1" label "X1"] edge[ source "X1" target "{0}"] node[ id "X2" label "X2"] edge[ source "X2" target "{0}"] edge[ source "X0" target "{1}"] edge[ source "X1" target "{1}"] edge[ source "X2" target "{1}"] node[ id "Z0" label "Z0"] edge[ source "Z0" target "{0}"]]'.format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input2(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """graph[ directed 1 node[ id "{0}" label "{0}" ] node [ id "{1}" label "{1}" ] node [ id "Unobserved Confounders" label "Unobserved Confounders" ] edge[ source "{0}" target "{1}" ] edge[ source "Unobserved Confounders" target "{0}" ] edge[ source "Unobserved Confounders" target "{1}" ] node[ id "X0" label "X0" ] edge[ source "X0" target "{0}" ] node[ id "X1" label "X1" ] edge[ source "X1" target "{0}" ] node[ id "X2" label "X2" ] edge[ source "X2" target "{0}" ] edge[ source "X0" target "{1}" ] edge[ source "X1" target "{1}" ] edge[ source "X2" target "{1}" ] node[ id "Z0" label "Z0" ] edge[ source "Z0" target "{0}" ]]""".format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input3(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """dag { "Unobserved Confounders" [pos="0.491,-1.056"] X0 [pos="-2.109,0.057"] X1 [adjusted, pos="-0.453,-1.562"] X2 [pos="-2.268,-1.210"] Z0 [pos="-1.918,-1.735"] v0 [latent, pos="-1.525,-1.293"] y [outcome, pos="-1.164,-0.116"] "Unobserved Confounders" -> v0 "Unobserved Confounders" -> y X0 -> v0 X0 -> y X1 -> v0 X1 -> y X2 -> v0 X2 -> y Z0 -> v0 v0 -> y } """ print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input4(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = "tests/sample_dag.txt" print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], ) graph_refutation_object = model.refute_graph( k=1, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == True @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation2(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] gml_str = """ graph [ directed 1 node [ id 0 label "a" ] node [ id 1 label "b" ] node [ id 2 label "c" ] node [ id 3 label "d" ] node [ id 4 label "e" ] node [ id 5 label "f" ] node [ id 6 label "g" ] node [ id 7 label "h" ] node [ id 8 label "i" ] node [ id 9 label "j" ] edge [ source 0 target 1 ] edge [ source 0 target 3 ] edge [ source 3 target 2 ] edge [ source 7 target 4 ] edge [ source 6 target 5 ] edge [ source 7 target 8 ] edge [ source 9 target 2 ] edge [ source 9 target 8 ] ] """ model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, ) graph_refutation_object = model.refute_graph( k=2, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == False if __name__ == "__main__": pytest.main([__file__])

import pandas as pd import pytest from pytest import mark from sklearn import linear_model import dowhy import dowhy.datasets from dowhy import CausalModel class TestCausalModel(object): @mark.parametrize( ["beta", "num_samples", "num_treatments"], [ (10, 100, 1), ], ) def test_external_estimator(self, beta, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) estimate = model.estimate_effect( identified_estimand, method_name="backdoor.tests.causal_estimators.mock_external_estimator.PropensityScoreWeightingEstimator", control_value=0, treatment_value=1, target_units="ate", # condition used for CATE confidence_intervals=True, method_params={"propensity_score_model": linear_model.LogisticRegression(max_iter=1000)}, ) assert estimate.estimator.propensity_score_model.max_iter == 1000 @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = 'graph[directed 1 node[ id "{0}" label "{0}"]node[ id "{1}" label "{1}"]node[ id "Unobserved Confounders" label "Unobserved Confounders"]edge[source "{0}" target "{1}"]edge[source "Unobserved Confounders" target "{0}"]edge[source "Unobserved Confounders" target "{1}"]node[ id "X0" label "X0"] edge[ source "X0" target "{0}"] node[ id "X1" label "X1"] edge[ source "X1" target "{0}"] node[ id "X2" label "X2"] edge[ source "X2" target "{0}"] edge[ source "X0" target "{1}"] edge[ source "X1" target "{1}"] edge[ source "X2" target "{1}"] node[ id "Z0" label "Z0"] edge[ source "Z0" target "{0}"]]'.format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input2(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """graph[ directed 1 node[ id "{0}" label "{0}" ] node [ id "{1}" label "{1}" ] node [ id "Unobserved Confounders" label "Unobserved Confounders" ] edge[ source "{0}" target "{1}" ] edge[ source "Unobserved Confounders" target "{0}" ] edge[ source "Unobserved Confounders" target "{1}" ] node[ id "X0" label "X0" ] edge[ source "X0" target "{0}" ] node[ id "X1" label "X1" ] edge[ source "X1" target "{0}" ] node[ id "X2" label "X2" ] edge[ source "X2" target "{0}" ] edge[ source "X0" target "{1}" ] edge[ source "X1" target "{1}" ] edge[ source "X2" target "{1}" ] node[ id "Z0" label "Z0" ] edge[ source "Z0" target "{0}" ]]""".format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input3(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """dag { "Unobserved Confounders" [pos="0.491,-1.056"] X0 [pos="-2.109,0.057"] X1 [adjusted, pos="-0.453,-1.562"] X2 [pos="-2.268,-1.210"] Z0 [pos="-1.918,-1.735"] v0 [latent, pos="-1.525,-1.293"] y [outcome, pos="-1.164,-0.116"] "Unobserved Confounders" -> v0 "Unobserved Confounders" -> y X0 -> v0 X0 -> y X1 -> v0 X1 -> y X2 -> v0 X2 -> y Z0 -> v0 v0 -> y } """ print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input4(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = "tests/sample_dag.txt" print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], ) graph_refutation_object = model.refute_graph( k=1, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == True @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation2(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] gml_str = """ graph [ directed 1 node [ id 0 label "a" ] node [ id 1 label "b" ] node [ id 2 label "c" ] node [ id 3 label "d" ] node [ id 4 label "e" ] node [ id 5 label "f" ] node [ id 6 label "g" ] node [ id 7 label "h" ] node [ id 8 label "i" ] node [ id 9 label "j" ] edge [ source 0 target 1 ] edge [ source 0 target 3 ] edge [ source 3 target 2 ] edge [ source 7 target 4 ] edge [ source 6 target 5 ] edge [ source 7 target 8 ] edge [ source 9 target 2 ] edge [ source 9 target 8 ] ] """ model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, ) graph_refutation_object = model.refute_graph( k=2, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == False def test_unobserved_graph_variables_log_warning(self, caplog): data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=3, num_instruments=1, num_effect_modifiers=1, num_samples=3, treatment_is_binary=True, stddev_treatment_noise=2, num_discrete_common_causes=1, ) df = data["df"] # Remove graph variable with name "W0" from observed data. df = df.drop(columns=["W0"]) expected_warning_message_regex = ( "1 variables are assumed unobserved because they are not in the " "dataset. Configure the logging level to `logging.WARNING` or " "higher for additional details." ) with pytest.warns( UserWarning, match=expected_warning_message_regex, ): _ = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], ) # Ensure that a log record exists that provides a more detailed view # of observed and unobserved graph variables (counts and variable names.) expected_logging_message = ( "The graph defines 7 variables. 6 were found in the dataset " "and will be analyzed as observed variables. 1 were not found " "in the dataset and will be analyzed as unobserved variables. " "The observed variables are: '['W1', 'W2', 'X0', 'Z0', 'v0', 'y']'. " "The unobserved variables are: '['W0']'. " "If this matches your expectations for observations, please continue. " "If you expected any of the unobserved variables to be in the " "dataframe, please check for typos." ) assert any( log_record for log_record in caplog.records if ( (log_record.name == "dowhy.causal_model") and (log_record.levelname == "WARNING") and (log_record.message == expected_logging_message) ) ), ( "Expected logging message informing about unobserved graph variables " "was not found. Expected a logging message to be emitted in module `dowhy.causal_model` " f"and with level `logging.WARNING` and this content '{expected_logging_message}'. " f"Only the following log records were emitted instead: '{caplog.records}'." ) if __name__ == "__main__": pytest.main([__file__])

MFreidank

2a2b3f4f7d02f8157d4b2ea39588b305e048eca8

23214a9850544780e21f0afecb390446ceca48a2

Were these whitespace edits intentional?

emrekiciman

py-why/dowhy

Enhancement: warn about unobserved graph variables in `causal_model.identify_effect`.

Closes #810. Introduces a `UserWarning` that is emitted if there are any graph variables that are not contained in the observed data (`self._data`). Adds a unit test for this implementation. Currently, the return values of `self.get_common_causes()`, `self.get_instruments()` and `self.get_effect_modifiers()` are considered as graph variables. In issue thread #810 there is also a suggestion to point out potential misspellings, for which I'd be happy to amend additional logic. See the questions in the last bullet point below to clarify the implementation in case we wish to add this. Design considerations and questions to reviewers: * Should we emit this via `self.logger.warning` instead? In my opinion, this will frequently point out improper usage (e.g., a typo in the columns of `self._data`) and hiding it in logging output that is not visible by default may not be desirable. But I'm open to suggestions. * Should this consider any other definition of *graph variables* than the one given above? * On handling misspellings (e.g., graph variable "AGE" vs data variable "AEG"): this would ideally use Levenshtein distance (e.g., with edit distance 1) to determine candidates. There are two options: using an external library (e.g., https://github.com/maxbachmann/Levenshtein) or a helper function. Which option is preferable? In case of a helper function, where would we best define it? Many thanks in advance for your help in pushing this feature across the finish line :) Best, MFreidank

2023-02-04 14:44:46+00:00

2023-02-14 20:21:29+00:00

tests/test_causal_model.py

import pandas as pd import pytest from pytest import mark from sklearn import linear_model import dowhy import dowhy.datasets from dowhy import CausalModel class TestCausalModel(object): @mark.parametrize( ["beta", "num_samples", "num_treatments"], [ (10, 100, 1), ], ) def test_external_estimator(self, beta, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) estimate = model.estimate_effect( identified_estimand, method_name="backdoor.tests.causal_estimators.mock_external_estimator.PropensityScoreWeightingEstimator", control_value=0, treatment_value=1, target_units="ate", # condition used for CATE confidence_intervals=True, method_params={"propensity_score_model": linear_model.LogisticRegression(max_iter=1000)}, ) assert estimate.estimator.propensity_score_model.max_iter == 1000 @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = 'graph[directed 1 node[ id "{0}" label "{0}"]node[ id "{1}" label "{1}"]node[ id "Unobserved Confounders" label "Unobserved Confounders"]edge[source "{0}" target "{1}"]edge[source "Unobserved Confounders" target "{0}"]edge[source "Unobserved Confounders" target "{1}"]node[ id "X0" label "X0"] edge[ source "X0" target "{0}"] node[ id "X1" label "X1"] edge[ source "X1" target "{0}"] node[ id "X2" label "X2"] edge[ source "X2" target "{0}"] edge[ source "X0" target "{1}"] edge[ source "X1" target "{1}"] edge[ source "X2" target "{1}"] node[ id "Z0" label "Z0"] edge[ source "Z0" target "{0}"]]'.format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input2(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """graph[ directed 1 node[ id "{0}" label "{0}" ] node [ id "{1}" label "{1}" ] node [ id "Unobserved Confounders" label "Unobserved Confounders" ] edge[ source "{0}" target "{1}" ] edge[ source "Unobserved Confounders" target "{0}" ] edge[ source "Unobserved Confounders" target "{1}" ] node[ id "X0" label "X0" ] edge[ source "X0" target "{0}" ] node[ id "X1" label "X1" ] edge[ source "X1" target "{0}" ] node[ id "X2" label "X2" ] edge[ source "X2" target "{0}" ] edge[ source "X0" target "{1}" ] edge[ source "X1" target "{1}" ] edge[ source "X2" target "{1}" ] node[ id "Z0" label "Z0" ] edge[ source "Z0" target "{0}" ]]""".format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input3(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """dag { "Unobserved Confounders" [pos="0.491,-1.056"] X0 [pos="-2.109,0.057"] X1 [adjusted, pos="-0.453,-1.562"] X2 [pos="-2.268,-1.210"] Z0 [pos="-1.918,-1.735"] v0 [latent, pos="-1.525,-1.293"] y [outcome, pos="-1.164,-0.116"] "Unobserved Confounders" -> v0 "Unobserved Confounders" -> y X0 -> v0 X0 -> y X1 -> v0 X1 -> y X2 -> v0 X2 -> y Z0 -> v0 v0 -> y } """ print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input4(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = "tests/sample_dag.txt" print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], ) graph_refutation_object = model.refute_graph( k=1, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == True @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation2(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] gml_str = """ graph [ directed 1 node [ id 0 label "a" ] node [ id 1 label "b" ] node [ id 2 label "c" ] node [ id 3 label "d" ] node [ id 4 label "e" ] node [ id 5 label "f" ] node [ id 6 label "g" ] node [ id 7 label "h" ] node [ id 8 label "i" ] node [ id 9 label "j" ] edge [ source 0 target 1 ] edge [ source 0 target 3 ] edge [ source 3 target 2 ] edge [ source 7 target 4 ] edge [ source 6 target 5 ] edge [ source 7 target 8 ] edge [ source 9 target 2 ] edge [ source 9 target 8 ] ] """ model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, ) graph_refutation_object = model.refute_graph( k=2, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == False if __name__ == "__main__": pytest.main([__file__])

import pandas as pd import pytest from pytest import mark from sklearn import linear_model import dowhy import dowhy.datasets from dowhy import CausalModel class TestCausalModel(object): @mark.parametrize( ["beta", "num_samples", "num_treatments"], [ (10, 100, 1), ], ) def test_external_estimator(self, beta, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) estimate = model.estimate_effect( identified_estimand, method_name="backdoor.tests.causal_estimators.mock_external_estimator.PropensityScoreWeightingEstimator", control_value=0, treatment_value=1, target_units="ate", # condition used for CATE confidence_intervals=True, method_params={"propensity_score_model": linear_model.LogisticRegression(max_iter=1000)}, ) assert estimate.estimator.propensity_score_model.max_iter == 1000 @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = 'graph[directed 1 node[ id "{0}" label "{0}"]node[ id "{1}" label "{1}"]node[ id "Unobserved Confounders" label "Unobserved Confounders"]edge[source "{0}" target "{1}"]edge[source "Unobserved Confounders" target "{0}"]edge[source "Unobserved Confounders" target "{1}"]node[ id "X0" label "X0"] edge[ source "X0" target "{0}"] node[ id "X1" label "X1"] edge[ source "X1" target "{0}"] node[ id "X2" label "X2"] edge[ source "X2" target "{0}"] edge[ source "X0" target "{1}"] edge[ source "X1" target "{1}"] edge[ source "X2" target "{1}"] node[ id "Z0" label "Z0"] edge[ source "Z0" target "{0}"]]'.format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input2(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """graph[ directed 1 node[ id "{0}" label "{0}" ] node [ id "{1}" label "{1}" ] node [ id "Unobserved Confounders" label "Unobserved Confounders" ] edge[ source "{0}" target "{1}" ] edge[ source "Unobserved Confounders" target "{0}" ] edge[ source "Unobserved Confounders" target "{1}" ] node[ id "X0" label "X0" ] edge[ source "X0" target "{0}" ] node[ id "X1" label "X1" ] edge[ source "X1" target "{0}" ] node[ id "X2" label "X2" ] edge[ source "X2" target "{0}" ] edge[ source "X0" target "{1}" ] edge[ source "X1" target "{1}" ] edge[ source "X2" target "{1}" ] node[ id "Z0" label "Z0" ] edge[ source "Z0" target "{0}" ]]""".format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input3(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """dag { "Unobserved Confounders" [pos="0.491,-1.056"] X0 [pos="-2.109,0.057"] X1 [adjusted, pos="-0.453,-1.562"] X2 [pos="-2.268,-1.210"] Z0 [pos="-1.918,-1.735"] v0 [latent, pos="-1.525,-1.293"] y [outcome, pos="-1.164,-0.116"] "Unobserved Confounders" -> v0 "Unobserved Confounders" -> y X0 -> v0 X0 -> y X1 -> v0 X1 -> y X2 -> v0 X2 -> y Z0 -> v0 v0 -> y } """ print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input4(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = "tests/sample_dag.txt" print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], ) graph_refutation_object = model.refute_graph( k=1, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == True @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation2(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] gml_str = """ graph [ directed 1 node [ id 0 label "a" ] node [ id 1 label "b" ] node [ id 2 label "c" ] node [ id 3 label "d" ] node [ id 4 label "e" ] node [ id 5 label "f" ] node [ id 6 label "g" ] node [ id 7 label "h" ] node [ id 8 label "i" ] node [ id 9 label "j" ] edge [ source 0 target 1 ] edge [ source 0 target 3 ] edge [ source 3 target 2 ] edge [ source 7 target 4 ] edge [ source 6 target 5 ] edge [ source 7 target 8 ] edge [ source 9 target 2 ] edge [ source 9 target 8 ] ] """ model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, ) graph_refutation_object = model.refute_graph( k=2, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == False def test_unobserved_graph_variables_log_warning(self, caplog): data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=3, num_instruments=1, num_effect_modifiers=1, num_samples=3, treatment_is_binary=True, stddev_treatment_noise=2, num_discrete_common_causes=1, ) df = data["df"] # Remove graph variable with name "W0" from observed data. df = df.drop(columns=["W0"]) expected_warning_message_regex = ( "1 variables are assumed unobserved because they are not in the " "dataset. Configure the logging level to `logging.WARNING` or " "higher for additional details." ) with pytest.warns( UserWarning, match=expected_warning_message_regex, ): _ = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], ) # Ensure that a log record exists that provides a more detailed view # of observed and unobserved graph variables (counts and variable names.) expected_logging_message = ( "The graph defines 7 variables. 6 were found in the dataset " "and will be analyzed as observed variables. 1 were not found " "in the dataset and will be analyzed as unobserved variables. " "The observed variables are: '['W1', 'W2', 'X0', 'Z0', 'v0', 'y']'. " "The unobserved variables are: '['W0']'. " "If this matches your expectations for observations, please continue. " "If you expected any of the unobserved variables to be in the " "dataframe, please check for typos." ) assert any( log_record for log_record in caplog.records if ( (log_record.name == "dowhy.causal_model") and (log_record.levelname == "WARNING") and (log_record.message == expected_logging_message) ) ), ( "Expected logging message informing about unobserved graph variables " "was not found. Expected a logging message to be emitted in module `dowhy.causal_model` " f"and with level `logging.WARNING` and this content '{expected_logging_message}'. " f"Only the following log records were emitted instead: '{caplog.records}'." ) if __name__ == "__main__": pytest.main([__file__])

MFreidank

2a2b3f4f7d02f8157d4b2ea39588b305e048eca8

23214a9850544780e21f0afecb390446ceca48a2

I believe this is causing the format check to fail in the build process.

emrekiciman

py-why/dowhy

Enhancement: warn about unobserved graph variables in `causal_model.identify_effect`.

Closes #810. Introduces a `UserWarning` that is emitted if there are any graph variables that are not contained in the observed data (`self._data`). Adds a unit test for this implementation. Currently, the return values of `self.get_common_causes()`, `self.get_instruments()` and `self.get_effect_modifiers()` are considered as graph variables. In issue thread #810 there is also a suggestion to point out potential misspellings, for which I'd be happy to amend additional logic. See the questions in the last bullet point below to clarify the implementation in case we wish to add this. Design considerations and questions to reviewers: * Should we emit this via `self.logger.warning` instead? In my opinion, this will frequently point out improper usage (e.g., a typo in the columns of `self._data`) and hiding it in logging output that is not visible by default may not be desirable. But I'm open to suggestions. * Should this consider any other definition of *graph variables* than the one given above? * On handling misspellings (e.g., graph variable "AGE" vs data variable "AEG"): this would ideally use Levenshtein distance (e.g., with edit distance 1) to determine candidates. There are two options: using an external library (e.g., https://github.com/maxbachmann/Levenshtein) or a helper function. Which option is preferable? In case of a helper function, where would we best define it? Many thanks in advance for your help in pushing this feature across the finish line :) Best, MFreidank

2023-02-04 14:44:46+00:00

2023-02-14 20:21:29+00:00

tests/test_causal_model.py

import pandas as pd import pytest from pytest import mark from sklearn import linear_model import dowhy import dowhy.datasets from dowhy import CausalModel class TestCausalModel(object): @mark.parametrize( ["beta", "num_samples", "num_treatments"], [ (10, 100, 1), ], ) def test_external_estimator(self, beta, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) estimate = model.estimate_effect( identified_estimand, method_name="backdoor.tests.causal_estimators.mock_external_estimator.PropensityScoreWeightingEstimator", control_value=0, treatment_value=1, target_units="ate", # condition used for CATE confidence_intervals=True, method_params={"propensity_score_model": linear_model.LogisticRegression(max_iter=1000)}, ) assert estimate.estimator.propensity_score_model.max_iter == 1000 @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = 'graph[directed 1 node[ id "{0}" label "{0}"]node[ id "{1}" label "{1}"]node[ id "Unobserved Confounders" label "Unobserved Confounders"]edge[source "{0}" target "{1}"]edge[source "Unobserved Confounders" target "{0}"]edge[source "Unobserved Confounders" target "{1}"]node[ id "X0" label "X0"] edge[ source "X0" target "{0}"] node[ id "X1" label "X1"] edge[ source "X1" target "{0}"] node[ id "X2" label "X2"] edge[ source "X2" target "{0}"] edge[ source "X0" target "{1}"] edge[ source "X1" target "{1}"] edge[ source "X2" target "{1}"] node[ id "Z0" label "Z0"] edge[ source "Z0" target "{0}"]]'.format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input2(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """graph[ directed 1 node[ id "{0}" label "{0}" ] node [ id "{1}" label "{1}" ] node [ id "Unobserved Confounders" label "Unobserved Confounders" ] edge[ source "{0}" target "{1}" ] edge[ source "Unobserved Confounders" target "{0}" ] edge[ source "Unobserved Confounders" target "{1}" ] node[ id "X0" label "X0" ] edge[ source "X0" target "{0}" ] node[ id "X1" label "X1" ] edge[ source "X1" target "{0}" ] node[ id "X2" label "X2" ] edge[ source "X2" target "{0}" ] edge[ source "X0" target "{1}" ] edge[ source "X1" target "{1}" ] edge[ source "X2" target "{1}" ] node[ id "Z0" label "Z0" ] edge[ source "Z0" target "{0}" ]]""".format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input3(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """dag { "Unobserved Confounders" [pos="0.491,-1.056"] X0 [pos="-2.109,0.057"] X1 [adjusted, pos="-0.453,-1.562"] X2 [pos="-2.268,-1.210"] Z0 [pos="-1.918,-1.735"] v0 [latent, pos="-1.525,-1.293"] y [outcome, pos="-1.164,-0.116"] "Unobserved Confounders" -> v0 "Unobserved Confounders" -> y X0 -> v0 X0 -> y X1 -> v0 X1 -> y X2 -> v0 X2 -> y Z0 -> v0 v0 -> y } """ print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input4(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = "tests/sample_dag.txt" print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], ) graph_refutation_object = model.refute_graph( k=1, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == True @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation2(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] gml_str = """ graph [ directed 1 node [ id 0 label "a" ] node [ id 1 label "b" ] node [ id 2 label "c" ] node [ id 3 label "d" ] node [ id 4 label "e" ] node [ id 5 label "f" ] node [ id 6 label "g" ] node [ id 7 label "h" ] node [ id 8 label "i" ] node [ id 9 label "j" ] edge [ source 0 target 1 ] edge [ source 0 target 3 ] edge [ source 3 target 2 ] edge [ source 7 target 4 ] edge [ source 6 target 5 ] edge [ source 7 target 8 ] edge [ source 9 target 2 ] edge [ source 9 target 8 ] ] """ model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, ) graph_refutation_object = model.refute_graph( k=2, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == False if __name__ == "__main__": pytest.main([__file__])

import pandas as pd import pytest from pytest import mark from sklearn import linear_model import dowhy import dowhy.datasets from dowhy import CausalModel class TestCausalModel(object): @mark.parametrize( ["beta", "num_samples", "num_treatments"], [ (10, 100, 1), ], ) def test_external_estimator(self, beta, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) estimate = model.estimate_effect( identified_estimand, method_name="backdoor.tests.causal_estimators.mock_external_estimator.PropensityScoreWeightingEstimator", control_value=0, treatment_value=1, target_units="ate", # condition used for CATE confidence_intervals=True, method_params={"propensity_score_model": linear_model.LogisticRegression(max_iter=1000)}, ) assert estimate.estimator.propensity_score_model.max_iter == 1000 @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = 'graph[directed 1 node[ id "{0}" label "{0}"]node[ id "{1}" label "{1}"]node[ id "Unobserved Confounders" label "Unobserved Confounders"]edge[source "{0}" target "{1}"]edge[source "Unobserved Confounders" target "{0}"]edge[source "Unobserved Confounders" target "{1}"]node[ id "X0" label "X0"] edge[ source "X0" target "{0}"] node[ id "X1" label "X1"] edge[ source "X1" target "{0}"] node[ id "X2" label "X2"] edge[ source "X2" target "{0}"] edge[ source "X0" target "{1}"] edge[ source "X1" target "{1}"] edge[ source "X2" target "{1}"] node[ id "Z0" label "Z0"] edge[ source "Z0" target "{0}"]]'.format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input2(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """graph[ directed 1 node[ id "{0}" label "{0}" ] node [ id "{1}" label "{1}" ] node [ id "Unobserved Confounders" label "Unobserved Confounders" ] edge[ source "{0}" target "{1}" ] edge[ source "Unobserved Confounders" target "{0}" ] edge[ source "Unobserved Confounders" target "{1}" ] node[ id "X0" label "X0" ] edge[ source "X0" target "{0}" ] node[ id "X1" label "X1" ] edge[ source "X1" target "{0}" ] node[ id "X2" label "X2" ] edge[ source "X2" target "{0}" ] edge[ source "X0" target "{1}" ] edge[ source "X1" target "{1}" ] edge[ source "X2" target "{1}" ] node[ id "Z0" label "Z0" ] edge[ source "Z0" target "{0}" ]]""".format( data["treatment_name"][0], data["outcome_name"] ) print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input3(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = """dag { "Unobserved Confounders" [pos="0.491,-1.056"] X0 [pos="-2.109,0.057"] X1 [adjusted, pos="-0.453,-1.562"] X2 [pos="-2.268,-1.210"] Z0 [pos="-1.918,-1.735"] v0 [latent, pos="-1.525,-1.293"] y [outcome, pos="-1.164,-0.116"] "Unobserved Confounders" -> v0 "Unobserved Confounders" -> y X0 -> v0 X0 -> y X1 -> v0 X1 -> y X2 -> v0 X2 -> y Z0 -> v0 v0 -> y } """ print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["beta", "num_instruments", "num_samples", "num_treatments"], [ (10, 1, 100, 1), ], ) def test_graph_input4(self, beta, num_instruments, num_samples, num_treatments): num_common_causes = 5 data = dowhy.datasets.linear_dataset( beta=beta, num_common_causes=num_common_causes, num_instruments=num_instruments, num_samples=num_samples, num_treatments=num_treatments, treatment_is_binary=True, ) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], proceed_when_unidentifiable=True, test_significance=None, ) # removing two common causes gml_str = "tests/sample_dag.txt" print(gml_str) model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, proceed_when_unidentifiable=True, test_significance=None, missing_nodes_as_confounders=True, ) common_causes = model.get_common_causes() assert all(node_name in common_causes for node_name in ["X1", "X2"]) all_nodes = model._graph.get_all_nodes(include_unobserved=True) assert all( node_name in all_nodes for node_name in ["Unobserved Confounders", "X0", "X1", "X2", "Z0", "v0", "y"] ) all_nodes = model._graph.get_all_nodes(include_unobserved=False) assert "Unobserved Confounders" not in all_nodes @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], ) graph_refutation_object = model.refute_graph( k=1, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == True @mark.parametrize( ["num_variables", "num_samples"], [ (10, 5000), ], ) def test_graph_refutation2(self, num_variables, num_samples): data = dowhy.datasets.dataset_from_random_graph(num_vars=num_variables, num_samples=num_samples) df = data["df"] gml_str = """ graph [ directed 1 node [ id 0 label "a" ] node [ id 1 label "b" ] node [ id 2 label "c" ] node [ id 3 label "d" ] node [ id 4 label "e" ] node [ id 5 label "f" ] node [ id 6 label "g" ] node [ id 7 label "h" ] node [ id 8 label "i" ] node [ id 9 label "j" ] edge [ source 0 target 1 ] edge [ source 0 target 3 ] edge [ source 3 target 2 ] edge [ source 7 target 4 ] edge [ source 6 target 5 ] edge [ source 7 target 8 ] edge [ source 9 target 2 ] edge [ source 9 target 8 ] ] """ model = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=gml_str, ) graph_refutation_object = model.refute_graph( k=2, independence_test={ "test_for_continuous": "partial_correlation", "test_for_discrete": "conditional_mutual_information", }, ) assert graph_refutation_object.refutation_result == False def test_unobserved_graph_variables_log_warning(self, caplog): data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=3, num_instruments=1, num_effect_modifiers=1, num_samples=3, treatment_is_binary=True, stddev_treatment_noise=2, num_discrete_common_causes=1, ) df = data["df"] # Remove graph variable with name "W0" from observed data. df = df.drop(columns=["W0"]) expected_warning_message_regex = ( "1 variables are assumed unobserved because they are not in the " "dataset. Configure the logging level to `logging.WARNING` or " "higher for additional details." ) with pytest.warns( UserWarning, match=expected_warning_message_regex, ): _ = CausalModel( data=df, treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"], ) # Ensure that a log record exists that provides a more detailed view # of observed and unobserved graph variables (counts and variable names.) expected_logging_message = ( "The graph defines 7 variables. 6 were found in the dataset " "and will be analyzed as observed variables. 1 were not found " "in the dataset and will be analyzed as unobserved variables. " "The observed variables are: '['W1', 'W2', 'X0', 'Z0', 'v0', 'y']'. " "The unobserved variables are: '['W0']'. " "If this matches your expectations for observations, please continue. " "If you expected any of the unobserved variables to be in the " "dataframe, please check for typos." ) assert any( log_record for log_record in caplog.records if ( (log_record.name == "dowhy.causal_model") and (log_record.levelname == "WARNING") and (log_record.message == expected_logging_message) ) ), ( "Expected logging message informing about unobserved graph variables " "was not found. Expected a logging message to be emitted in module `dowhy.causal_model` " f"and with level `logging.WARNING` and this content '{expected_logging_message}'. " f"Only the following log records were emitted instead: '{caplog.records}'." ) if __name__ == "__main__": pytest.main([__file__])

MFreidank

2a2b3f4f7d02f8157d4b2ea39588b305e048eca8

23214a9850544780e21f0afecb390446ceca48a2

No, they weren't intentional. Will look into fixing this, might have been caused by some editor auto-formatting.

MFreidank

py-why/dowhy

Rewriting the User Guide

Hi all, This is a first stab at unifying the user guide for effect estimation and gcm sub-package. This is an extremely early draft and will require a lot of iterations before we can put it into the right place. I'm already publishing it here to avoid going in the wrong direction and wasting time. To simplify iterations, I put everything into one big markdown. Once we're happy with the result, we'd move it into proper rst structure. The basic idea behind this guide is that we identify commonalities and differences between effect estimation and gcm. The obvious common part is the causal graph usually defined using NetworkX in one way or another. This is covered in the **Modeling Causal Relations** sections. After explaining the basic concepts of how systems can be modeled as graphs, we directly go to a task-based structure, i.e. we lead the reader through the difference parts of DoWhy by letting them focus on the specific causal task they want to perform. Having this as markdown allows us to comment on very specific portions of the document. For a better overview of how the sections are structured, see this TOC: <img width="177" alt="Screen Shot 2023-01-27 at 16 35 34" src="https://user-images.githubusercontent.com/3618401/215125476-e7ea5938-5269-438b-ac9d-c2e2b882d799.png">

2023-01-27 15:39:34+00:00

2023-07-27 18:47:39+00:00

docs/source/user_guide/intro.rst

Introduction to DoWhy ===================== The need for causal inference ---------------------------------- Predictive models uncover patterns that connect the inputs and outcome in observed data. To intervene, however, we need to estimate the effect of changing an input from its current value, for which no data exists. Such questions, involving estimating a *counterfactual*, are common in decision-making scenarios. * Will it work? * Does a proposed change to a system improve people's outcomes? * Why did it work? * What led to a change in a system's outcome? * What should we do? * What changes to a system are likely to improve outcomes for people? * What are the overall effects? * How does the system interact with human behavior? * What is the effect of a system's recommendations on people's activity? Answering these questions requires causal reasoning. While many methods exist for causal inference, it is hard to compare their assumptions and robustness of results. DoWhy makes three contributions, 1. Provides a principled way of modeling a given problem as a causal graph so that all assumptions are explicit. 2. Provides a unified interface for many popular causal inference methods, combining the two major frameworks of graphical models and potential outcomes. 3. Automatically tests for the validity of assumptions if possible and assesses the robustness of the estimate to violations. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. Sample causal inference analysis in DoWhy ------------------------------------------- Most DoWhy analyses for causal inference take 4 lines to write, assuming a pandas dataframe df that contains the data: .. code:: python from dowhy import CausalModel import dowhy.datasets # Load some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000, treatment_is_binary=True) DoWhy supports two formats for providing the causal graph: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. After loading in the data, we use the four main operations in DoWhy: *model*, *estimate*, *identify* and *refute*: .. code:: python # I. Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # II. Identify causal effect and return target estimands identified_estimand = model.identify_effect() # III. Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # IV. Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") DoWhy stresses on the interpretability of its output. At any point in the analysis, you can inspect the untested assumptions, identified estimands (if any) and the estimate (if any). Here's a sample output of the linear regression estimator. .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/regression_output.png For a full code example, check out the `Getting Started with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. You can also use Conditional Average Treatment Effect (CATE) estimation methods from other libraries such as EconML and CausalML, as shown in the `Conditional Treatment Effects <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. For more examples of using DoWhy, check out the Jupyter notebooks in `docs/source/example_notebooks <https://github.com/microsoft/dowhy/tree/main/docs/source/example_notebooks/>`_ or try them online at `Binder <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. GCM-based inference (experimental) ---------------------------------- Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy. For details, check out the `documentation for the gcm sub-package <https://py-why.github.io/dowhy/gcm>`_. The basic recipe for this API works as follows: .. code:: python # 1. Modeling cause-effect relationships as a structural causal model # (causal graph + functional causal models): scm = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z scm.set_causal_mechanism('X', gcm.EmpiricalDistribution()) scm.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) scm.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) # 2. Fitting the SCM to the data: gcm.fit(scm, data) # 3. Answering a causal query based on the SCM: results = gcm.<causal_query>(scm, ...) Where <causal_query> can be one of multiple functions explained in `Answering Causal Questions <https://py-why.github.io/dowhy/gcm/user_guide/answering_causal_questions/index.html>`_.

Introduction to DoWhy ===================== Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, prediction, quantification of causal influences, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. A key feature of DoWhy is its refutation API that can test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Additionally, DoWhy supports answering causal questions beyond effect estimation by utilizing graphical causal models, which enable tackling problems such as root cause analysis or quantification of causal influences. Supported causal tasks ---------------------- DoWhy's API is organized around the different *causal tasks* that it enables a user to perform. We categorize tasks into :doc:`causal_tasks/estimating_causal_effects/index`, :doc:`causal_tasks/causal_prediction/index`, :doc:`causal_tasks/root_causing_and_explaining/index`, and :doc:`causal_tasks/what_if/index`. These tasks give answers to questions, such as "If I change the color of my button to red, how much will this change users’ purchase decisions?", or "Which service in my distributed system has caused the frontend to be slower than usual?". To perform tasks, DoWhy leverages two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO), depending on the task at hand. What’s common to most tasks is that they require a *causal graph*, which is modeled after the problem domain. For that reason, this user guide starts with :doc:`modeling_causal_relations/index`. Readers interested in :doc:`causal_tasks/root_causing_and_explaining/unit_change` or :doc:`causal_tasks/root_causing_and_explaining/feature_relevance`, which do not necessarily require a causal graph, can skip right to those sections. To aid the navigation within this user guide and the library further, the following flow chart can be used: .. image:: navigation.png :alt: Visual navigation map to aid the user in navigating the user guide :width: 100% Testing validity of a causal analysis ------------------------------------- Since causal tasks concern an interventional data distribution that is often not observed, we need special ways to evaluate the validity of a causal estimate. Methods like cross-validation from predictive machine learning do not work, unless we have access to samples from the interventional distribution. Therefore, for each causal task, a important part of the analysis is to test whether the obtained answer is valid. In DoWhy, we call this process *refutation*, which involves refuting or challenging the assumptions made by a causal analysis. Refutations are performed at two stages: after modeling the causal graph, and after completing the analysis for a task. In the first stage, graph refutations test whether the assumptions encoded in a given causal graph are valid. This is an important set of refutations since all downstream analysis depends on the graph. These refutations are typically task-agnostic and we recommend running them to improve the quality of the assumed graph. DoWhy's functionality for refuting a causal graph is described in :doc:`modeling_causal_relations/refuting_causal_graph/index`. The second kind of refutations, estimate refutations, are conducted after the task analysis returns a causal estimate. These refutations test whether the analysis follows best practices, provides the correct answer under special test data, and how robust the final estimate is to violation of assumptions. Estimate refutations can help improve the robustness of an analysis or help choose between multiple candidate models in the analysis. We discuss estimate refutations in a separate chapter, :doc:`refuting_causal_estimates/index`. For an alternative approach of validating a given causal graph, see `Falsification of User-Given Directed Acyclic Graphs <../example_notebooks/gcm_falsify_dag.html>`_. Who this user guide is for -------------------------- If you are new to causal inference, this user guide helps you understand the difference causal tasks and provides examples on how to implement them using DoWhy. If you are familiar with causal inference, you can jump right into code examples. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/py-why/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. For an introductory example of root-cause analysis, check out the `Root Cause Analysis in a Microservice Architecture notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/gcm_rca_microservice_architecture.ipynb>`_. For a full list of example notebooks, see `Example notebooks <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks>`_.

petergtz

ccc4af28684f251d457c740d502f1e3e0da327fd

0df1f4c5d2f737dd70bacfaf00058b1da1d5dbf9

Can also link the examples here. Maybe something along the line of "See also the example notebooks[Link] how to use them in a concrete problem."

bloebp

py-why/dowhy

Rewriting the User Guide

Hi all, This is a first stab at unifying the user guide for effect estimation and gcm sub-package. This is an extremely early draft and will require a lot of iterations before we can put it into the right place. I'm already publishing it here to avoid going in the wrong direction and wasting time. To simplify iterations, I put everything into one big markdown. Once we're happy with the result, we'd move it into proper rst structure. The basic idea behind this guide is that we identify commonalities and differences between effect estimation and gcm. The obvious common part is the causal graph usually defined using NetworkX in one way or another. This is covered in the **Modeling Causal Relations** sections. After explaining the basic concepts of how systems can be modeled as graphs, we directly go to a task-based structure, i.e. we lead the reader through the difference parts of DoWhy by letting them focus on the specific causal task they want to perform. Having this as markdown allows us to comment on very specific portions of the document. For a better overview of how the sections are structured, see this TOC: <img width="177" alt="Screen Shot 2023-01-27 at 16 35 34" src="https://user-images.githubusercontent.com/3618401/215125476-e7ea5938-5269-438b-ac9d-c2e2b882d799.png">

2023-01-27 15:39:34+00:00

2023-07-27 18:47:39+00:00

docs/source/user_guide/intro.rst

Introduction to DoWhy ===================== The need for causal inference ---------------------------------- Predictive models uncover patterns that connect the inputs and outcome in observed data. To intervene, however, we need to estimate the effect of changing an input from its current value, for which no data exists. Such questions, involving estimating a *counterfactual*, are common in decision-making scenarios. * Will it work? * Does a proposed change to a system improve people's outcomes? * Why did it work? * What led to a change in a system's outcome? * What should we do? * What changes to a system are likely to improve outcomes for people? * What are the overall effects? * How does the system interact with human behavior? * What is the effect of a system's recommendations on people's activity? Answering these questions requires causal reasoning. While many methods exist for causal inference, it is hard to compare their assumptions and robustness of results. DoWhy makes three contributions, 1. Provides a principled way of modeling a given problem as a causal graph so that all assumptions are explicit. 2. Provides a unified interface for many popular causal inference methods, combining the two major frameworks of graphical models and potential outcomes. 3. Automatically tests for the validity of assumptions if possible and assesses the robustness of the estimate to violations. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. Sample causal inference analysis in DoWhy ------------------------------------------- Most DoWhy analyses for causal inference take 4 lines to write, assuming a pandas dataframe df that contains the data: .. code:: python from dowhy import CausalModel import dowhy.datasets # Load some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000, treatment_is_binary=True) DoWhy supports two formats for providing the causal graph: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. After loading in the data, we use the four main operations in DoWhy: *model*, *estimate*, *identify* and *refute*: .. code:: python # I. Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # II. Identify causal effect and return target estimands identified_estimand = model.identify_effect() # III. Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # IV. Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") DoWhy stresses on the interpretability of its output. At any point in the analysis, you can inspect the untested assumptions, identified estimands (if any) and the estimate (if any). Here's a sample output of the linear regression estimator. .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/regression_output.png For a full code example, check out the `Getting Started with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. You can also use Conditional Average Treatment Effect (CATE) estimation methods from other libraries such as EconML and CausalML, as shown in the `Conditional Treatment Effects <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. For more examples of using DoWhy, check out the Jupyter notebooks in `docs/source/example_notebooks <https://github.com/microsoft/dowhy/tree/main/docs/source/example_notebooks/>`_ or try them online at `Binder <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. GCM-based inference (experimental) ---------------------------------- Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy. For details, check out the `documentation for the gcm sub-package <https://py-why.github.io/dowhy/gcm>`_. The basic recipe for this API works as follows: .. code:: python # 1. Modeling cause-effect relationships as a structural causal model # (causal graph + functional causal models): scm = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z scm.set_causal_mechanism('X', gcm.EmpiricalDistribution()) scm.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) scm.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) # 2. Fitting the SCM to the data: gcm.fit(scm, data) # 3. Answering a causal query based on the SCM: results = gcm.<causal_query>(scm, ...) Where <causal_query> can be one of multiple functions explained in `Answering Causal Questions <https://py-why.github.io/dowhy/gcm/user_guide/answering_causal_questions/index.html>`_.

Introduction to DoWhy ===================== Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, prediction, quantification of causal influences, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. A key feature of DoWhy is its refutation API that can test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Additionally, DoWhy supports answering causal questions beyond effect estimation by utilizing graphical causal models, which enable tackling problems such as root cause analysis or quantification of causal influences. Supported causal tasks ---------------------- DoWhy's API is organized around the different *causal tasks* that it enables a user to perform. We categorize tasks into :doc:`causal_tasks/estimating_causal_effects/index`, :doc:`causal_tasks/causal_prediction/index`, :doc:`causal_tasks/root_causing_and_explaining/index`, and :doc:`causal_tasks/what_if/index`. These tasks give answers to questions, such as "If I change the color of my button to red, how much will this change users’ purchase decisions?", or "Which service in my distributed system has caused the frontend to be slower than usual?". To perform tasks, DoWhy leverages two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO), depending on the task at hand. What’s common to most tasks is that they require a *causal graph*, which is modeled after the problem domain. For that reason, this user guide starts with :doc:`modeling_causal_relations/index`. Readers interested in :doc:`causal_tasks/root_causing_and_explaining/unit_change` or :doc:`causal_tasks/root_causing_and_explaining/feature_relevance`, which do not necessarily require a causal graph, can skip right to those sections. To aid the navigation within this user guide and the library further, the following flow chart can be used: .. image:: navigation.png :alt: Visual navigation map to aid the user in navigating the user guide :width: 100% Testing validity of a causal analysis ------------------------------------- Since causal tasks concern an interventional data distribution that is often not observed, we need special ways to evaluate the validity of a causal estimate. Methods like cross-validation from predictive machine learning do not work, unless we have access to samples from the interventional distribution. Therefore, for each causal task, a important part of the analysis is to test whether the obtained answer is valid. In DoWhy, we call this process *refutation*, which involves refuting or challenging the assumptions made by a causal analysis. Refutations are performed at two stages: after modeling the causal graph, and after completing the analysis for a task. In the first stage, graph refutations test whether the assumptions encoded in a given causal graph are valid. This is an important set of refutations since all downstream analysis depends on the graph. These refutations are typically task-agnostic and we recommend running them to improve the quality of the assumed graph. DoWhy's functionality for refuting a causal graph is described in :doc:`modeling_causal_relations/refuting_causal_graph/index`. The second kind of refutations, estimate refutations, are conducted after the task analysis returns a causal estimate. These refutations test whether the analysis follows best practices, provides the correct answer under special test data, and how robust the final estimate is to violation of assumptions. Estimate refutations can help improve the robustness of an analysis or help choose between multiple candidate models in the analysis. We discuss estimate refutations in a separate chapter, :doc:`refuting_causal_estimates/index`. For an alternative approach of validating a given causal graph, see `Falsification of User-Given Directed Acyclic Graphs <../example_notebooks/gcm_falsify_dag.html>`_. Who this user guide is for -------------------------- If you are new to causal inference, this user guide helps you understand the difference causal tasks and provides examples on how to implement them using DoWhy. If you are familiar with causal inference, you can jump right into code examples. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/py-why/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. For an introductory example of root-cause analysis, check out the `Root Cause Analysis in a Microservice Architecture notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/gcm_rca_microservice_architecture.ipynb>`_. For a full list of example notebooks, see `Example notebooks <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks>`_.

petergtz

ccc4af28684f251d457c740d502f1e3e0da327fd

0df1f4c5d2f737dd70bacfaf00058b1da1d5dbf9

Suggestion: To perform tasks, DoWhy leverages two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO), depending on the task at hand. What’s common to most tasks is that they require a causal graph, which is modeled after the problem domain. For that reason, this user guide starts with :doc:`modeling_causal_relations/index`. Readers interested in :doc:`causal_tasks/root_causing_and_explaining/unit_change` or :doc:`causal_tasks/root_causing_and_explaining/feature_attribution`, which do not require a causal graph, can skip right to those sections.

bloebp

py-why/dowhy

Rewriting the User Guide

Hi all, This is a first stab at unifying the user guide for effect estimation and gcm sub-package. This is an extremely early draft and will require a lot of iterations before we can put it into the right place. I'm already publishing it here to avoid going in the wrong direction and wasting time. To simplify iterations, I put everything into one big markdown. Once we're happy with the result, we'd move it into proper rst structure. The basic idea behind this guide is that we identify commonalities and differences between effect estimation and gcm. The obvious common part is the causal graph usually defined using NetworkX in one way or another. This is covered in the **Modeling Causal Relations** sections. After explaining the basic concepts of how systems can be modeled as graphs, we directly go to a task-based structure, i.e. we lead the reader through the difference parts of DoWhy by letting them focus on the specific causal task they want to perform. Having this as markdown allows us to comment on very specific portions of the document. For a better overview of how the sections are structured, see this TOC: <img width="177" alt="Screen Shot 2023-01-27 at 16 35 34" src="https://user-images.githubusercontent.com/3618401/215125476-e7ea5938-5269-438b-ac9d-c2e2b882d799.png">

2023-01-27 15:39:34+00:00

2023-07-27 18:47:39+00:00

docs/source/user_guide/intro.rst

Introduction to DoWhy ===================== The need for causal inference ---------------------------------- Predictive models uncover patterns that connect the inputs and outcome in observed data. To intervene, however, we need to estimate the effect of changing an input from its current value, for which no data exists. Such questions, involving estimating a *counterfactual*, are common in decision-making scenarios. * Will it work? * Does a proposed change to a system improve people's outcomes? * Why did it work? * What led to a change in a system's outcome? * What should we do? * What changes to a system are likely to improve outcomes for people? * What are the overall effects? * How does the system interact with human behavior? * What is the effect of a system's recommendations on people's activity? Answering these questions requires causal reasoning. While many methods exist for causal inference, it is hard to compare their assumptions and robustness of results. DoWhy makes three contributions, 1. Provides a principled way of modeling a given problem as a causal graph so that all assumptions are explicit. 2. Provides a unified interface for many popular causal inference methods, combining the two major frameworks of graphical models and potential outcomes. 3. Automatically tests for the validity of assumptions if possible and assesses the robustness of the estimate to violations. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. Sample causal inference analysis in DoWhy ------------------------------------------- Most DoWhy analyses for causal inference take 4 lines to write, assuming a pandas dataframe df that contains the data: .. code:: python from dowhy import CausalModel import dowhy.datasets # Load some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000, treatment_is_binary=True) DoWhy supports two formats for providing the causal graph: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. After loading in the data, we use the four main operations in DoWhy: *model*, *estimate*, *identify* and *refute*: .. code:: python # I. Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # II. Identify causal effect and return target estimands identified_estimand = model.identify_effect() # III. Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # IV. Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") DoWhy stresses on the interpretability of its output. At any point in the analysis, you can inspect the untested assumptions, identified estimands (if any) and the estimate (if any). Here's a sample output of the linear regression estimator. .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/regression_output.png For a full code example, check out the `Getting Started with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. You can also use Conditional Average Treatment Effect (CATE) estimation methods from other libraries such as EconML and CausalML, as shown in the `Conditional Treatment Effects <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. For more examples of using DoWhy, check out the Jupyter notebooks in `docs/source/example_notebooks <https://github.com/microsoft/dowhy/tree/main/docs/source/example_notebooks/>`_ or try them online at `Binder <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. GCM-based inference (experimental) ---------------------------------- Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy. For details, check out the `documentation for the gcm sub-package <https://py-why.github.io/dowhy/gcm>`_. The basic recipe for this API works as follows: .. code:: python # 1. Modeling cause-effect relationships as a structural causal model # (causal graph + functional causal models): scm = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z scm.set_causal_mechanism('X', gcm.EmpiricalDistribution()) scm.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) scm.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) # 2. Fitting the SCM to the data: gcm.fit(scm, data) # 3. Answering a causal query based on the SCM: results = gcm.<causal_query>(scm, ...) Where <causal_query> can be one of multiple functions explained in `Answering Causal Questions <https://py-why.github.io/dowhy/gcm/user_guide/answering_causal_questions/index.html>`_.

Introduction to DoWhy ===================== Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, prediction, quantification of causal influences, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. A key feature of DoWhy is its refutation API that can test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Additionally, DoWhy supports answering causal questions beyond effect estimation by utilizing graphical causal models, which enable tackling problems such as root cause analysis or quantification of causal influences. Supported causal tasks ---------------------- DoWhy's API is organized around the different *causal tasks* that it enables a user to perform. We categorize tasks into :doc:`causal_tasks/estimating_causal_effects/index`, :doc:`causal_tasks/causal_prediction/index`, :doc:`causal_tasks/root_causing_and_explaining/index`, and :doc:`causal_tasks/what_if/index`. These tasks give answers to questions, such as "If I change the color of my button to red, how much will this change users’ purchase decisions?", or "Which service in my distributed system has caused the frontend to be slower than usual?". To perform tasks, DoWhy leverages two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO), depending on the task at hand. What’s common to most tasks is that they require a *causal graph*, which is modeled after the problem domain. For that reason, this user guide starts with :doc:`modeling_causal_relations/index`. Readers interested in :doc:`causal_tasks/root_causing_and_explaining/unit_change` or :doc:`causal_tasks/root_causing_and_explaining/feature_relevance`, which do not necessarily require a causal graph, can skip right to those sections. To aid the navigation within this user guide and the library further, the following flow chart can be used: .. image:: navigation.png :alt: Visual navigation map to aid the user in navigating the user guide :width: 100% Testing validity of a causal analysis ------------------------------------- Since causal tasks concern an interventional data distribution that is often not observed, we need special ways to evaluate the validity of a causal estimate. Methods like cross-validation from predictive machine learning do not work, unless we have access to samples from the interventional distribution. Therefore, for each causal task, a important part of the analysis is to test whether the obtained answer is valid. In DoWhy, we call this process *refutation*, which involves refuting or challenging the assumptions made by a causal analysis. Refutations are performed at two stages: after modeling the causal graph, and after completing the analysis for a task. In the first stage, graph refutations test whether the assumptions encoded in a given causal graph are valid. This is an important set of refutations since all downstream analysis depends on the graph. These refutations are typically task-agnostic and we recommend running them to improve the quality of the assumed graph. DoWhy's functionality for refuting a causal graph is described in :doc:`modeling_causal_relations/refuting_causal_graph/index`. The second kind of refutations, estimate refutations, are conducted after the task analysis returns a causal estimate. These refutations test whether the analysis follows best practices, provides the correct answer under special test data, and how robust the final estimate is to violation of assumptions. Estimate refutations can help improve the robustness of an analysis or help choose between multiple candidate models in the analysis. We discuss estimate refutations in a separate chapter, :doc:`refuting_causal_estimates/index`. For an alternative approach of validating a given causal graph, see `Falsification of User-Given Directed Acyclic Graphs <../example_notebooks/gcm_falsify_dag.html>`_. Who this user guide is for -------------------------- If you are new to causal inference, this user guide helps you understand the difference causal tasks and provides examples on how to implement them using DoWhy. If you are familiar with causal inference, you can jump right into code examples. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/py-why/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. For an introductory example of root-cause analysis, check out the `Root Cause Analysis in a Microservice Architecture notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/gcm_rca_microservice_architecture.ipynb>`_. For a full list of example notebooks, see `Example notebooks <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks>`_.

petergtz

ccc4af28684f251d457c740d502f1e3e0da327fd

0df1f4c5d2f737dd70bacfaf00058b1da1d5dbf9

Comments on the new image: Its really great! Two things: - Can maybe more generally say “Quantifying causal contributions” or something along the line instead of specifically ICC, seeing that we also have direct arrow strength. - Would it make sense to add an optional validation/refutation step? Although this might be difficult seeing that this happens after the estimation step in case of effect estimation.

bloebp

py-why/dowhy

Rewriting the User Guide

Hi all, This is a first stab at unifying the user guide for effect estimation and gcm sub-package. This is an extremely early draft and will require a lot of iterations before we can put it into the right place. I'm already publishing it here to avoid going in the wrong direction and wasting time. To simplify iterations, I put everything into one big markdown. Once we're happy with the result, we'd move it into proper rst structure. The basic idea behind this guide is that we identify commonalities and differences between effect estimation and gcm. The obvious common part is the causal graph usually defined using NetworkX in one way or another. This is covered in the **Modeling Causal Relations** sections. After explaining the basic concepts of how systems can be modeled as graphs, we directly go to a task-based structure, i.e. we lead the reader through the difference parts of DoWhy by letting them focus on the specific causal task they want to perform. Having this as markdown allows us to comment on very specific portions of the document. For a better overview of how the sections are structured, see this TOC: <img width="177" alt="Screen Shot 2023-01-27 at 16 35 34" src="https://user-images.githubusercontent.com/3618401/215125476-e7ea5938-5269-438b-ac9d-c2e2b882d799.png">

2023-01-27 15:39:34+00:00

2023-07-27 18:47:39+00:00

docs/source/user_guide/intro.rst

Introduction to DoWhy ===================== The need for causal inference ---------------------------------- Predictive models uncover patterns that connect the inputs and outcome in observed data. To intervene, however, we need to estimate the effect of changing an input from its current value, for which no data exists. Such questions, involving estimating a *counterfactual*, are common in decision-making scenarios. * Will it work? * Does a proposed change to a system improve people's outcomes? * Why did it work? * What led to a change in a system's outcome? * What should we do? * What changes to a system are likely to improve outcomes for people? * What are the overall effects? * How does the system interact with human behavior? * What is the effect of a system's recommendations on people's activity? Answering these questions requires causal reasoning. While many methods exist for causal inference, it is hard to compare their assumptions and robustness of results. DoWhy makes three contributions, 1. Provides a principled way of modeling a given problem as a causal graph so that all assumptions are explicit. 2. Provides a unified interface for many popular causal inference methods, combining the two major frameworks of graphical models and potential outcomes. 3. Automatically tests for the validity of assumptions if possible and assesses the robustness of the estimate to violations. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. Sample causal inference analysis in DoWhy ------------------------------------------- Most DoWhy analyses for causal inference take 4 lines to write, assuming a pandas dataframe df that contains the data: .. code:: python from dowhy import CausalModel import dowhy.datasets # Load some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000, treatment_is_binary=True) DoWhy supports two formats for providing the causal graph: `gml <https://github.com/GunterMueller/UNI_PASSAU_FMI_Graph_Drawing>`_ (preferred) and `dot <http://www.graphviz.org/documentation/>`_. After loading in the data, we use the four main operations in DoWhy: *model*, *estimate*, *identify* and *refute*: .. code:: python # I. Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # II. Identify causal effect and return target estimands identified_estimand = model.identify_effect() # III. Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # IV. Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") DoWhy stresses on the interpretability of its output. At any point in the analysis, you can inspect the untested assumptions, identified estimands (if any) and the estimate (if any). Here's a sample output of the linear regression estimator. .. image:: https://raw.githubusercontent.com/microsoft/dowhy/main/docs/images/regression_output.png For a full code example, check out the `Getting Started with DoWhy <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_simple_example.ipynb>`_ notebook. You can also use Conditional Average Treatment Effect (CATE) estimation methods from other libraries such as EconML and CausalML, as shown in the `Conditional Treatment Effects <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb>`_ notebook. For more examples of using DoWhy, check out the Jupyter notebooks in `docs/source/example_notebooks <https://github.com/microsoft/dowhy/tree/main/docs/source/example_notebooks/>`_ or try them online at `Binder <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. GCM-based inference (experimental) ---------------------------------- Graphical causal model-based inference, or GCM-based inference for short, is an experimental addition to DoWhy. For details, check out the `documentation for the gcm sub-package <https://py-why.github.io/dowhy/gcm>`_. The basic recipe for this API works as follows: .. code:: python # 1. Modeling cause-effect relationships as a structural causal model # (causal graph + functional causal models): scm = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z scm.set_causal_mechanism('X', gcm.EmpiricalDistribution()) scm.set_causal_mechanism('Y', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) scm.set_causal_mechanism('Z', gcm.AdditiveNoiseModel(gcm.ml.create_linear_regressor())) # 2. Fitting the SCM to the data: gcm.fit(scm, data) # 3. Answering a causal query based on the SCM: results = gcm.<causal_query>(scm, ...) Where <causal_query> can be one of multiple functions explained in `Answering Causal Questions <https://py-why.github.io/dowhy/gcm/user_guide/answering_causal_questions/index.html>`_.

Introduction to DoWhy ===================== Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, prediction, quantification of causal influences, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. A key feature of DoWhy is its refutation API that can test causal assumptions for any estimation method, thus making inference more robust and accessible to non-experts. DoWhy supports estimation of the average causal effect for backdoor, frontdoor, instrumental variable and other identification methods, and estimation of the conditional effect (CATE) through an integration with the EconML library. Additionally, DoWhy supports answering causal questions beyond effect estimation by utilizing graphical causal models, which enable tackling problems such as root cause analysis or quantification of causal influences. Supported causal tasks ---------------------- DoWhy's API is organized around the different *causal tasks* that it enables a user to perform. We categorize tasks into :doc:`causal_tasks/estimating_causal_effects/index`, :doc:`causal_tasks/causal_prediction/index`, :doc:`causal_tasks/root_causing_and_explaining/index`, and :doc:`causal_tasks/what_if/index`. These tasks give answers to questions, such as "If I change the color of my button to red, how much will this change users’ purchase decisions?", or "Which service in my distributed system has caused the frontend to be slower than usual?". To perform tasks, DoWhy leverages two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO), depending on the task at hand. What’s common to most tasks is that they require a *causal graph*, which is modeled after the problem domain. For that reason, this user guide starts with :doc:`modeling_causal_relations/index`. Readers interested in :doc:`causal_tasks/root_causing_and_explaining/unit_change` or :doc:`causal_tasks/root_causing_and_explaining/feature_relevance`, which do not necessarily require a causal graph, can skip right to those sections. To aid the navigation within this user guide and the library further, the following flow chart can be used: .. image:: navigation.png :alt: Visual navigation map to aid the user in navigating the user guide :width: 100% Testing validity of a causal analysis ------------------------------------- Since causal tasks concern an interventional data distribution that is often not observed, we need special ways to evaluate the validity of a causal estimate. Methods like cross-validation from predictive machine learning do not work, unless we have access to samples from the interventional distribution. Therefore, for each causal task, a important part of the analysis is to test whether the obtained answer is valid. In DoWhy, we call this process *refutation*, which involves refuting or challenging the assumptions made by a causal analysis. Refutations are performed at two stages: after modeling the causal graph, and after completing the analysis for a task. In the first stage, graph refutations test whether the assumptions encoded in a given causal graph are valid. This is an important set of refutations since all downstream analysis depends on the graph. These refutations are typically task-agnostic and we recommend running them to improve the quality of the assumed graph. DoWhy's functionality for refuting a causal graph is described in :doc:`modeling_causal_relations/refuting_causal_graph/index`. The second kind of refutations, estimate refutations, are conducted after the task analysis returns a causal estimate. These refutations test whether the analysis follows best practices, provides the correct answer under special test data, and how robust the final estimate is to violation of assumptions. Estimate refutations can help improve the robustness of an analysis or help choose between multiple candidate models in the analysis. We discuss estimate refutations in a separate chapter, :doc:`refuting_causal_estimates/index`. For an alternative approach of validating a given causal graph, see `Falsification of User-Given Directed Acyclic Graphs <../example_notebooks/gcm_falsify_dag.html>`_. Who this user guide is for -------------------------- If you are new to causal inference, this user guide helps you understand the difference causal tasks and provides examples on how to implement them using DoWhy. If you are familiar with causal inference, you can jump right into code examples. To see DoWhy in action, check out how it can be applied to estimate the effect of a subscription or rewards program for customers [`Rewards notebook <https://github.com/microsoft/py-why/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_] and for implementing and evaluating causal inference methods on benchmark datasets like the `Infant Health and Development Program (IHDP) <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_ihdp_data_example.ipynb>`_ dataset, `Infant Mortality (Twins) <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_twins_example.ipynb>`_ dataset, and the `Lalonde Jobs <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_lalonde_example.ipynb>`_ dataset. For an introductory example of root-cause analysis, check out the `Root Cause Analysis in a Microservice Architecture notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/gcm_rca_microservice_architecture.ipynb>`_. For a full list of example notebooks, see `Example notebooks <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks>`_.

petergtz

ccc4af28684f251d457c740d502f1e3e0da327fd

0df1f4c5d2f737dd70bacfaf00058b1da1d5dbf9

> Can maybe more generally say “Quantifying causal contributions” or something along the line instead of specifically ICC, seeing that we also have direct arrow strength. Yes. The PowerPoint presentation (which acts as source for this png) is alongside everything else. Just open it, make the necessary changes and take a screenshot of the final result (sorry, PP's export features are a bit limited, but I like the easy editing of PP). Make the screenshot rather too big than too small to make sure it looks crisp when rendered in the docs. > Would it make sense to add an optional validation/refutation step? Although this might be difficult seeing that this happens after the estimation step in case of effect estimation. Yes, I think that makes sense. Same is true for the validation of GCMs. The fact that this is a b it hard to model visually, might also be an indicator that not everything is perfect API-wise, or documentation-wise, or about how we think about this stuff. So it's definitely open for iteration. OTOH, I wouldn't over-engineer the graphic, because it would lose its simplicity for navigation. I'm sure we can find a middleground.

petergtz

py-why/dowhy

Pin Numpy version to 1.23.1

This makes it compatible with Numba version 0.56.4. The way the Numpy version was specified before, installs version 1.24.0 which is incompatible with Numba, see also https://github.com/numba/numba/pull/8691. Numba is a transient dependency coming in through `econml` and `sparse`. The resulting error looks like this: ``` Python 3.9.16 (main, Dec 24 2022, 07:02:54) [GCC 7.3.1 20180712 (Red Hat 7.3.1-15)] on linux Type "help", "copyright", "credits" or "license" for more information. >>> import dowhy Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/var/task/dowhy/__init__.py", line 4, in <module> from dowhy.causal_model import CausalModel File "/var/task/dowhy/causal_model.py", line 10, in <module> import dowhy.causal_refuters as causal_refuters File "/var/task/dowhy/causal_refuters/__init__.py", line 5, in <module> from dowhy.causal_refuters.add_unobserved_common_cause import ( File "/var/task/dowhy/causal_refuters/add_unobserved_common_cause.py", line 22, in <module> from dowhy.causal_refuters.non_parametric_sensitivity_analyzer import NonParametricSensitivityAnalyzer File "/var/task/dowhy/causal_refuters/non_parametric_sensitivity_analyzer.py", line 14, in <module> from dowhy.causal_refuters.reisz import get_alpha_estimator File "/var/task/dowhy/causal_refuters/reisz.py", line 2, in <module> from econml.grf._base_grf import BaseGRF File "/var/task/econml/grf/__init__.py", line 14, in <module> from ._criterion import LinearMomentGRFCriterion, LinearMomentGRFCriterionMSE File "econml/grf/_criterion.pyx", line 1, in init econml.grf._criterion File "/var/task/econml/tree/__init__.py", line 8, in <module> from ._tree_classes import BaseTree File "/var/task/econml/tree/_tree_classes.py", line 11, in <module> from ..utilities import deprecated File "/var/task/econml/utilities.py", line 9, in <module> import sparse as sp File "/var/task/sparse/__init__.py", line 1, in <module> from ._coo import COO, as_coo File "/var/task/sparse/_coo/__init__.py", line 1, in <module> from .core import COO, as_coo File "/var/task/sparse/_coo/core.py", line 9, in <module> import numba File "/var/task/numba/__init__.py", line 42, in <module> from numba.np.ufunc import (vectorize, guvectorize, threading_layer, File "/var/task/numba/np/ufunc/__init__.py", line 3, in <module> from numba.np.ufunc.decorators import Vectorize, GUVectorize, vectorize, guvectorize File "/var/task/numba/np/ufunc/decorators.py", line 3, in <module> from numba.np.ufunc import _internal SystemError: initialization of _internal failed without raising an exception ``` **Complete version information to reproduce this error scenario:** ``` Package Version ----------------------------- --------- alabaster 0.7.13 awslambdaric 2.0.4 Babel 2.11.0 boto3 1.26.55 botocore 1.29.55 causal-learn 0.1.3.1 certifi 2022.12.7 charset-normalizer 3.0.1 cloudpickle 2.2.1 contourpy 1.0.7 cycler 0.11.0 Cython 0.29.33 docutils 0.19 dowhy 0.9.1 econml 0.14.0 fonttools 4.38.0 graphviz 0.20.1 idna 3.4 imagesize 1.4.1 importlib-metadata 6.0.0 Jinja2 3.1.2 jmespath 1.0.1 joblib 1.2.0 kiwisolver 1.4.4 lightgbm 3.3.4 llvmlite 0.39.1 MarkupSafe 2.1.2 matplotlib 3.6.3 mpmath 1.2.1 networkx 3.0 numba 0.56.4 numpy 1.24.1 packaging 23.0 pandas 1.5.3 patsy 0.5.3 Pillow 9.4.0 pydot 1.4.2 Pygments 2.14.0 pyparsing 3.0.9 python-dateutil 2.8.2 pytz 2022.7.1 requests 2.28.2 s3transfer 0.6.0 scikit-learn 1.2.0 scipy 1.10.0 seaborn 0.12.2 setuptools 66.1.1 shap 0.40.0 simplejson 3.17.2 six 1.16.0 slicer 0.0.7 snowballstemmer 2.2.0 sparse 0.13.0 Sphinx 5.3.0 sphinx_design 0.3.0 sphinxcontrib-applehelp 1.0.4 sphinxcontrib-devhelp 1.0.2 sphinxcontrib-htmlhelp 2.0.0 sphinxcontrib-jsmath 1.0.1 sphinxcontrib-qthelp 1.0.3 sphinxcontrib-serializinghtml 1.1.5 statsmodels 0.13.5 sympy 1.11.1 threadpoolctl 3.1.0 tqdm 4.64.1 typing_extensions 4.4.0 urllib3 1.26.14 wheel 0.38.4 zipp 3.11.0 ```

2023-01-24 09:37:39+00:00

2023-01-26 16:19:34+00:00

pyproject.toml

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = ["PyWhy Community <amshar@microsoft.com>"] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/py-why/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', 'Programming Language :: Python :: 3.10', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model', ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [build-system] requires = ["poetry-core>=1.0.0"] build-backend = "poetry.core.masonry.api" [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * autogluon requires scikit-learn <1.2.0 # * numba (imported by econml) requires python <3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.11" cython = "^0.29.32" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "<1.2.0" pydot = { version = "^1.4.2", optional = true } joblib = "^1.1.0" pygraphviz = { version = "^1.9", optional = true } econml = { version = "*" } tqdm = "^4.64.0" causal-learn = "^0.1.3.0" autogluon-tabular = { extras = [ "all", ], version = "^0.6.0", optional = true, python = "<3.10" } #Plotting Extra matplotlib = { version = "^3.5.3", optional = true } sphinx_design = "^0.3.0" cvxpy = "^1.2.2" [tool.poetry.extras] pygraphviz = ["pygraphviz"] pydot = ["pydot"] plotting = ["matplotlib"] autogluon = ["autogluon-tabular"] [tool.poetry.group.dev.dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = { version = "^22.6.0", extras = ["jupyter"] } isort = "^5.10.1" pytest = "^7.1.2" pytest-cov = "^3.0.0" pytest-split = "^0.8.0" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" keras = "^2.9.0" xgboost = "^1.7.0" mypy = "^0.971" torch = "^1.12.1" torchvision = "^0.13.1" pytorch-lightning = "^1.7.7" [tool.poetry.group.docs] optional = true [tool.poetry.group.docs.dependencies] # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx = "^5.3.0" sphinxcontrib-googleanalytics = { git = "https://github.com/sphinx-contrib/googleanalytics.git", branch = "master" } nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" ipykernel = "^6.15.1" sphinx-copybutton = "0.5.0" seaborn = "^0.12.1" tensorflow = "^2.11.0" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = { version = "7.0.0rc3", allow-prereleases = true } [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates.", "notebook: jupyter notebook tests", "focused: a debug marker to focus on specific tests", ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' _black_check = 'black --check .' _isort_check = 'isort --check .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_durations = "poetry run poe test --store-durations" test_advanced = "pytest -v" test_focused = "pytest -v -m 'focused'" [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.format_check] sequence = ['_black_check', '_isort_check'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'format_check', 'test'] ignore_fail = "return_non_zero" [tool.black] line-length = 120 target-version = ['py38'] include = '\.pyi?$' extend-exclude = ''' ( __pycache__ | \.github ) ''' [tool.pylint] max-line-length = 120 disable = ["W0511"] [tool.isort] profile = 'black' multi_line_output = 3 line_length = 120 py_version = 38

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = ["PyWhy Community <amshar@microsoft.com>"] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/py-why/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', 'Programming Language :: Python :: 3.10', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model', ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [build-system] requires = ["poetry-core>=1.0.0"] build-backend = "poetry.core.masonry.api" [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * autogluon requires scikit-learn <1.2.0 # * numba (imported by econml) requires python <3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.11" cython = "^0.29.32" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "<1.2.0" pydot = { version = "^1.4.2", optional = true } joblib = "^1.1.0" pygraphviz = { version = "^1.9", optional = true } econml = { version = "*" } tqdm = "^4.64.0" causal-learn = "^0.1.3.0" autogluon-tabular = { extras = [ "all", ], version = "^0.6.0", optional = true, python = "<3.10" } #Plotting Extra matplotlib = { version = "^3.5.3", optional = true } sphinx_design = "^0.3.0" cvxpy = "^1.2.2" [tool.poetry.extras] pygraphviz = ["pygraphviz"] pydot = ["pydot"] plotting = ["matplotlib"] autogluon = ["autogluon-tabular"] [tool.poetry.group.dev.dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = { version = "^22.6.0", extras = ["jupyter"] } isort = "^5.10.1" pytest = "^7.1.2" pytest-cov = "^3.0.0" pytest-split = "^0.8.0" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" keras = "^2.9.0" xgboost = "^1.7.0" mypy = "^0.971" torch = "^1.12.1" torchvision = "^0.13.1" pytorch-lightning = "^1.7.7" [tool.poetry.group.docs] optional = true [tool.poetry.group.docs.dependencies] # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx = "^5.3.0" sphinxcontrib-googleanalytics = { git = "https://github.com/sphinx-contrib/googleanalytics.git", branch = "master" } nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" ipykernel = "^6.15.1" sphinx-copybutton = "0.5.0" seaborn = "^0.12.1" tensorflow = "^2.11.0" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = { version = "7.0.0rc3", allow-prereleases = true } [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates.", "notebook: jupyter notebook tests", "focused: a debug marker to focus on specific tests", ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' _black_check = 'black --check .' _isort_check = 'isort --check .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_durations = "poetry run poe test --store-durations" test_advanced = "pytest -v" test_focused = "pytest -v -m 'focused'" [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.format_check] sequence = ['_black_check', '_isort_check'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'format_check', 'test'] ignore_fail = "return_non_zero" [tool.black] line-length = 120 target-version = ['py38'] include = '\.pyi?$' extend-exclude = ''' ( __pycache__ | \.github ) ''' [tool.pylint] max-line-length = 120 disable = ["W0511"] [tool.isort] profile = 'black' multi_line_output = 3 line_length = 120 py_version = 38

petergtz

96a055ae4448ecddeb458d86b10588ea3295c4a3

ca340303e993fa4be1831f74afccf9161e19a9d8

I don't think the `==` is strictly necessary here. With semver you can just remove the `^` symbol to match the explicit version.

darthtrevino

py-why/dowhy

Enhancement/remove data from estimators

* Remove data, treatment and outcome from estimator object * estimate_effect now have data, treatment and outcome as parameters

2023-01-03 18:39:35+00:00

2023-01-20 11:06:39+00:00

dowhy/causal_estimator.py

import copy import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: bool = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **_, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._target_estimand = identified_estimand self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._confidence_intervals = confidence_intervals # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = need_conditional_estimates self._bootstrap_estimates = None self._bootstrap_null_estimates = None def _set_data(self, data: pd.DataFrame, treatment_name: List[str], outcome_name: List[str]): """Sets the data for the estimator :param data: data frame containing the data :param treatment_name: name of the treatment variable :param outcome_name: name of the outcome variable """ self._data = data self._treatment_name = treatment_name self._outcome_name = outcome_name[0] self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] def _set_effect_modifiers(self, effect_modifier_names: Optional[List[str]] = None): """Sets the effect modifiers for the estimator Modifies need_conditional_estimates accordingly to effect modifiers value :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._effect_modifiers = effect_modifier_names if effect_modifier_names is not None: self._effect_modifier_names = [cname for cname in effect_modifier_names if cname in self._data.columns] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = [] else: self._effect_modifier_names = [] self.need_conditional_estimates = ( self.need_conditional_estimates if self.need_conditional_estimates != "auto" else (self._effect_modifier_names and len(self._effect_modifier_names) > 0) ) def _set_identified_estimand(self, new_identified_estimand): """Method used internally to change the target estimand (required by some refuters) :param new_identified_estimand: The new target_estimand to use """ self._target_estimand = new_identified_estimand def get_new_estimator_object( self, identified_estimand, test_significance=False, evaluate_effect_strength=False, confidence_intervals=None, ): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with the identified_estimand :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :returns: A new instance of the same estimator class that had generated the given estimate. """ new_estimator = copy.deepcopy(self) new_estimator._target_estimand = identified_estimand new_estimator._test_significance = test_significance new_estimator._evaluate_effect_strength = evaluate_effect_strength new_estimator._confidence_intervals = ( self._confidence_intervals if confidence_intervals is None else confidence_intervals ) return new_estimator def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = self.get_new_estimator_object( self._target_estimand, # names of treatment and outcome test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, ) new_estimator.fit( new_data, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, effect_modifier_names=self._effect_modifier_names, ) new_effect = new_estimator.estimate_effect( treatment_value=self._treatment_value, control_value=self._control_value, target_units=self._target_units, ) simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = self.get_new_estimator_object( self._target_estimand, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, ) new_estimator.fit( data=new_data, treatment_name=self._target_estimand.treatment_variable, outcome_name=("dummy_outcome",), effect_modifier_names=self._effect_modifier_names, ) new_effect = new_estimator.estimate_effect( target_units=self._target_units, ) null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( data: pd.DataFrame, treatment: Union[str, List[str]], outcome: Union[str, List[str]], identifier_name: str, estimator: CausalEstimator, control_value: int = 0, treatment_value: int = 1, target_units: str = "ate", effect_modifiers: List[str] = None, fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param estimator: Instance of a CausalEstimator to use :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None: effect_modifiers = [] treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = estimator.__class__ identified_estimand = estimator._target_estimand identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) if fit_estimator: estimator.fit( data=data, treatment_name=treatment, outcome_name=outcome, effect_modifier_names=effect_modifiers, **method_params["fit_params"] if "fit_params" in method_params else {}, ) estimate = estimator.estimate_effect( treatment_value=treatment_value, control_value=control_value, target_units=target_units, confidence_intervals=estimator._confidence_intervals, ) # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=estimator._significance_test, evaluate_effect_strength=estimator._effect_strength_eval, confidence_intervals=estimator._confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, ) if estimator._significance_test: estimator.test_significance(estimate.value, method=estimator._significance_test) if estimator._confidence_intervals: estimator.estimate_confidence_intervals( estimate.value, confidence_level=estimator.confidence_level, method=estimator._confidence_intervals ) if estimator._effect_strength_eval: effect_strength_dict = estimator.evaluate_effect_strength(estimate) estimate.add_effect_strength(effect_strength_dict) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import copy import logging from collections import namedtuple from dataclasses import dataclass from typing import Any, Dict, List, Optional, Tuple, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: Union[bool, str] = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **_, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._target_estimand = identified_estimand self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._confidence_intervals = confidence_intervals # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = need_conditional_estimates self._bootstrap_estimates = None self._bootstrap_null_estimates = None def _set_effect_modifiers(self, data: pd.DataFrame, effect_modifier_names: Optional[List[str]] = None): """Sets the effect modifiers for the estimator Modifies need_conditional_estimates accordingly to effect modifiers value :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._effect_modifiers = effect_modifier_names if effect_modifier_names is not None: self._effect_modifier_names = [cname for cname in effect_modifier_names if cname in data.columns] if len(self._effect_modifier_names) > 0: self._effect_modifiers = data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = [] else: self._effect_modifier_names = [] self.need_conditional_estimates = ( self.need_conditional_estimates if self.need_conditional_estimates != "auto" else (self._effect_modifier_names and len(self._effect_modifier_names) > 0) ) def _set_identified_estimand(self, new_identified_estimand): """Method used internally to change the target estimand (required by some refuters) :param new_identified_estimand: The new target_estimand to use """ self._target_estimand = new_identified_estimand def get_new_estimator_object( self, identified_estimand, test_significance=False, evaluate_effect_strength=False, confidence_intervals=None, ): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with the identified_estimand :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :returns: A new instance of the same estimator class that had generated the given estimate. """ new_estimator = copy.deepcopy(self) new_estimator._target_estimand = identified_estimand new_estimator._test_significance = test_significance new_estimator._effect_strength_eval = evaluate_effect_strength new_estimator._confidence_intervals = ( self._confidence_intervals if confidence_intervals is None else confidence_intervals ) return new_estimator def estimate_effect_naive(self, data: pd.DataFrame): """ :param data: Pandas dataframe to estimate effect """ # TODO Only works for binary treatment df_withtreatment = data.loc[data[self._target_estimand.treatment_variable] == 1] df_notreatment = data.loc[data[self._target_estimand.treatment_variable] == 0] est = np.mean(df_withtreatment[self._target_estimand.outcome_variable]) - np.mean( df_notreatment[self._target_estimand.outcome_variable] ) return CausalEstimate(data, None, None, est, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects( self, data: pd.DataFrame, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None ): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param data: Pandas dataframe to calculate the conditional effects :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(data[em].dtypes): data[prefix + str(em)] = pd.qcut(data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, data: pd.DataFrame, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(data)) if sample_size > len(data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(data, n_samples=sample_size) new_estimator = self.get_new_estimator_object( self._target_estimand, # names of treatment and outcome test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, ) new_estimator.fit( new_data, effect_modifier_names=self._effect_modifier_names, ) new_effect = new_estimator.estimate_effect( new_data, treatment_value=self._treatment_value, control_value=self._control_value, target_units=self._target_units, ) simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, data: pd.DataFrame, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None, ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(data, num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(data, num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals( self, data: pd.DataFrame, estimate_value, confidence_level=None, method=None, **kwargs ): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( data, estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( data, estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, data: pd.DataFrame, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(data, num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(data, num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, data: pd.DataFrame, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(data, **kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(data, **kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, data: pd.DataFrame, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(data[self._target_estimand.outcome_variable]) new_data = data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = self.get_new_estimator_object( self._target_estimand, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, ) new_estimator.fit( data=new_data, effect_modifier_names=self._effect_modifier_names, ) new_effect = new_estimator.estimate_effect( new_data, target_units=self._target_units, ) null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, data: pd.DataFrame, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(data, estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(data, estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, data: pd.DataFrame, estimate): fraction_effect_explained = self._evaluate_effect_strength(data, estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, data: pd.DataFrame, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive(data) self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( data: pd.DataFrame, treatment: Union[str, List[str]], outcome: Union[str, List[str]], identifier_name: str, estimator: CausalEstimator, control_value: int = 0, treatment_value: int = 1, target_units: str = "ate", effect_modifiers: List[str] = None, fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param estimator: Instance of a CausalEstimator to use :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None: effect_modifiers = [] treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = estimator.__class__ identified_estimand = estimator._target_estimand identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( None, None, None, 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate( None, None, None, None, None, control_value=control_value, treatment_value=treatment_value ) if fit_estimator: estimator.fit( data=data, effect_modifier_names=effect_modifiers, **method_params["fit_params"] if "fit_params" in method_params else {}, ) estimate = estimator.estimate_effect( data, treatment_value=treatment_value, control_value=control_value, target_units=target_units, confidence_intervals=estimator._confidence_intervals, ) if estimator._significance_test: estimator.test_significance(data, estimate.value, method=estimator._significance_test) if estimator._confidence_intervals: estimator.estimate_confidence_intervals( data, estimate.value, confidence_level=estimator.confidence_level, method=estimator._confidence_intervals, ) if estimator._effect_strength_eval: effect_strength_dict = estimator.evaluate_effect_strength(data, estimate) estimate.add_effect_strength(effect_strength_dict) # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=estimator._significance_test, evaluate_effect_strength=estimator._effect_strength_eval, confidence_intervals=estimator._confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, data, treatment_name, outcome_name, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): # TODO: Remove _data, _treatment_name and _outcome_name from this object # we save them here to enable the methods that required these properties saved in the estimator # eventually we should call those methods and just save the results in this object # instead of having this object invoke the estimator methods with the data. self._data = data self._treatment_name = treatment_name self._outcome_name = outcome_name self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( data=self._data, estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs, ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(self._data, method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self._data, self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format( self.estimator.signif_results_tostr(self.test_stat_significance(self._data)) ) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals(self._data) ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

325cf4e245de3e55b85a42c5fefc36f6ef34db46

c3e1c75696a8297aa48977ea4c7b7e8dc50dc6aa

do we require treatment_name as a parameter here since it can be inferred from self? In general, I think it is okay for internal methods that start with _ to require this argument, but definitely user-facing methods can avoid it.

amit-sharma

py-why/dowhy

Enhancement/remove data from estimators

* Remove data, treatment and outcome from estimator object * estimate_effect now have data, treatment and outcome as parameters

2023-01-03 18:39:35+00:00

2023-01-20 11:06:39+00:00

dowhy/causal_estimator.py

import copy import logging from collections import namedtuple from typing import Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: bool = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **_, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._target_estimand = identified_estimand self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._confidence_intervals = confidence_intervals # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = need_conditional_estimates self._bootstrap_estimates = None self._bootstrap_null_estimates = None def _set_data(self, data: pd.DataFrame, treatment_name: List[str], outcome_name: List[str]): """Sets the data for the estimator :param data: data frame containing the data :param treatment_name: name of the treatment variable :param outcome_name: name of the outcome variable """ self._data = data self._treatment_name = treatment_name self._outcome_name = outcome_name[0] self._treatment = self._data[self._treatment_name] self._outcome = self._data[self._outcome_name] def _set_effect_modifiers(self, effect_modifier_names: Optional[List[str]] = None): """Sets the effect modifiers for the estimator Modifies need_conditional_estimates accordingly to effect modifiers value :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._effect_modifiers = effect_modifier_names if effect_modifier_names is not None: self._effect_modifier_names = [cname for cname in effect_modifier_names if cname in self._data.columns] if len(self._effect_modifier_names) > 0: self._effect_modifiers = self._data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = [] else: self._effect_modifier_names = [] self.need_conditional_estimates = ( self.need_conditional_estimates if self.need_conditional_estimates != "auto" else (self._effect_modifier_names and len(self._effect_modifier_names) > 0) ) def _set_identified_estimand(self, new_identified_estimand): """Method used internally to change the target estimand (required by some refuters) :param new_identified_estimand: The new target_estimand to use """ self._target_estimand = new_identified_estimand def get_new_estimator_object( self, identified_estimand, test_significance=False, evaluate_effect_strength=False, confidence_intervals=None, ): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with the identified_estimand :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :returns: A new instance of the same estimator class that had generated the given estimate. """ new_estimator = copy.deepcopy(self) new_estimator._target_estimand = identified_estimand new_estimator._test_significance = test_significance new_estimator._evaluate_effect_strength = evaluate_effect_strength new_estimator._confidence_intervals = ( self._confidence_intervals if confidence_intervals is None else confidence_intervals ) return new_estimator def estimate_effect_naive(self): # TODO Only works for binary treatment df_withtreatment = self._data.loc[self._data[self._treatment_name] == 1] df_notreatment = self._data.loc[self._data[self._treatment_name] == 0] est = np.mean(df_withtreatment[self._outcome_name]) - np.mean(df_notreatment[self._outcome_name]) return CausalEstimate(est, None, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects(self, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(self._data[em].dtypes): self._data[prefix + str(em)] = pd.qcut(self._data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = self._data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): self._data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(self._data)) if sample_size > len(self._data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(self._data, n_samples=sample_size) new_estimator = self.get_new_estimator_object( self._target_estimand, # names of treatment and outcome test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, ) new_estimator.fit( new_data, self._target_estimand.treatment_variable, self._target_estimand.outcome_variable, effect_modifier_names=self._effect_modifier_names, ) new_effect = new_estimator.estimate_effect( treatment_value=self._treatment_value, control_value=self._control_value, target_units=self._target_units, ) simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals(self, estimate_value, confidence_level=None, method=None, **kwargs): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(**kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(self._outcome) new_data = self._data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = self.get_new_estimator_object( self._target_estimand, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, ) new_estimator.fit( data=new_data, treatment_name=self._target_estimand.treatment_variable, outcome_name=("dummy_outcome",), effect_modifier_names=self._effect_modifier_names, ) new_effect = new_estimator.estimate_effect( target_units=self._target_units, ) null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, estimate): fraction_effect_explained = self._evaluate_effect_strength(estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive() self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( data: pd.DataFrame, treatment: Union[str, List[str]], outcome: Union[str, List[str]], identifier_name: str, estimator: CausalEstimator, control_value: int = 0, treatment_value: int = 1, target_units: str = "ate", effect_modifiers: List[str] = None, fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param estimator: Instance of a CausalEstimator to use :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None: effect_modifiers = [] treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = estimator.__class__ identified_estimand = estimator._target_estimand identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate(None, None, None, control_value=control_value, treatment_value=treatment_value) if fit_estimator: estimator.fit( data=data, treatment_name=treatment, outcome_name=outcome, effect_modifier_names=effect_modifiers, **method_params["fit_params"] if "fit_params" in method_params else {}, ) estimate = estimator.estimate_effect( treatment_value=treatment_value, control_value=control_value, target_units=target_units, confidence_intervals=estimator._confidence_intervals, ) # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=estimator._significance_test, evaluate_effect_strength=estimator._effect_strength_eval, confidence_intervals=estimator._confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, ) if estimator._significance_test: estimator.test_significance(estimate.value, method=estimator._significance_test) if estimator._confidence_intervals: estimator.estimate_confidence_intervals( estimate.value, confidence_level=estimator.confidence_level, method=estimator._confidence_intervals ) if estimator._effect_strength_eval: effect_strength_dict = estimator.evaluate_effect_strength(estimate) estimate.add_effect_strength(effect_strength_dict) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret() def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format(self.estimator.signif_results_tostr(self.test_stat_significance())) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals() ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

import copy import logging from collections import namedtuple from dataclasses import dataclass from typing import Any, Dict, List, Optional, Tuple, Union import numpy as np import pandas as pd import sympy as sp from sklearn.utils import resample import dowhy.interpreters as interpreters from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand from dowhy.utils.api import parse_state logger = logging.getLogger(__name__) class CausalEstimator: """Base class for an estimator of causal effect. Subclasses implement different estimation methods. All estimation methods are in the package "dowhy.causal_estimators" """ # The default number of simulations for statistical testing DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST = 1000 # The default number of simulations to obtain confidence intervals DEFAULT_NUMBER_OF_SIMULATIONS_CI = 100 # The portion of the total size that should be taken each time to find the confidence intervals # 1 is the recommended value # https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf # https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 DEFAULT_SAMPLE_SIZE_FRACTION = 1 # The default Confidence Level DEFAULT_CONFIDENCE_LEVEL = 0.95 # Number of quantiles to discretize continuous columns, for applying groupby NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS = 5 # Prefix to add to temporary categorical variables created after discretization TEMP_CAT_COLUMN_PREFIX = "__categorical__" DEFAULT_NOTIMPLEMENTEDERROR_MSG = "not yet implemented for {0}. If you would this to be implemented in the next version, please raise an issue at https://github.com/microsoft/dowhy/issues" BootstrapEstimates = namedtuple("BootstrapEstimates", ["estimates", "params"]) DEFAULT_INTERPRET_METHOD = ["textual_effect_interpreter"] # std args to be removed from locals() before being passed to args_dict _STD_INIT_ARGS = ("self", "__class__", "args", "kwargs") def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: Union[bool, str] = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **_, ): """Initializes an estimator with data and names of relevant variables. This method is called from the constructors of its child classes. :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters :returns: an instance of the estimator class. """ self._target_estimand = identified_estimand self._significance_test = test_significance self._effect_strength_eval = evaluate_effect_strength self._confidence_intervals = confidence_intervals # Setting the default interpret method self.interpret_method = CausalEstimator.DEFAULT_INTERPRET_METHOD self.logger = logging.getLogger(__name__) # Check if some parameters were set, otherwise set to default values self.num_null_simulations = num_null_simulations self.num_simulations = num_simulations self.sample_size_fraction = sample_size_fraction self.confidence_level = confidence_level self.num_quantiles_to_discretize_cont_cols = num_quantiles_to_discretize_cont_cols # Estimate conditional estimates by default self.need_conditional_estimates = need_conditional_estimates self._bootstrap_estimates = None self._bootstrap_null_estimates = None def _set_effect_modifiers(self, data: pd.DataFrame, effect_modifier_names: Optional[List[str]] = None): """Sets the effect modifiers for the estimator Modifies need_conditional_estimates accordingly to effect modifiers value :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._effect_modifiers = effect_modifier_names if effect_modifier_names is not None: self._effect_modifier_names = [cname for cname in effect_modifier_names if cname in data.columns] if len(self._effect_modifier_names) > 0: self._effect_modifiers = data[self._effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self.logger.debug("Effect modifiers: " + ",".join(self._effect_modifier_names)) else: self._effect_modifier_names = [] else: self._effect_modifier_names = [] self.need_conditional_estimates = ( self.need_conditional_estimates if self.need_conditional_estimates != "auto" else (self._effect_modifier_names and len(self._effect_modifier_names) > 0) ) def _set_identified_estimand(self, new_identified_estimand): """Method used internally to change the target estimand (required by some refuters) :param new_identified_estimand: The new target_estimand to use """ self._target_estimand = new_identified_estimand def get_new_estimator_object( self, identified_estimand, test_significance=False, evaluate_effect_strength=False, confidence_intervals=None, ): """Create a new estimator of the same type as the one passed in the estimate argument. Creates a new object with the identified_estimand :param identified_estimand: IdentifiedEstimand An instance of the identified estimand class that provides the information with respect to which causal pathways are employed when the treatment effects the outcome :returns: A new instance of the same estimator class that had generated the given estimate. """ new_estimator = copy.deepcopy(self) new_estimator._target_estimand = identified_estimand new_estimator._test_significance = test_significance new_estimator._effect_strength_eval = evaluate_effect_strength new_estimator._confidence_intervals = ( self._confidence_intervals if confidence_intervals is None else confidence_intervals ) return new_estimator def estimate_effect_naive(self, data: pd.DataFrame): """ :param data: Pandas dataframe to estimate effect """ # TODO Only works for binary treatment df_withtreatment = data.loc[data[self._target_estimand.treatment_variable] == 1] df_notreatment = data.loc[data[self._target_estimand.treatment_variable] == 0] est = np.mean(df_withtreatment[self._target_estimand.outcome_variable]) - np.mean( df_notreatment[self._target_estimand.outcome_variable] ) return CausalEstimate(data, None, None, est, None, control_value=0, treatment_value=1) def _estimate_effect_fn(self, data_df): """Function used in conditional effect estimation. This function is to be overridden by each child estimator. The overridden function should take in a dataframe as input and return the estimate for that data. """ raise NotImplementedError( ("Conditional treatment effects are " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format( self.__class__ ) ) def _estimate_conditional_effects( self, data: pd.DataFrame, estimate_effect_fn, effect_modifier_names=None, num_quantiles=None ): """Estimate conditional treatment effects. Common method for all estimators that utilizes a specific estimate_effect_fn implemented by each child estimator. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param data: Pandas dataframe to calculate the conditional effects :param estimate_effect_fn: Function that has a single parameter (a data frame) and returns the treatment effect estimate on that data. :param effect_modifier_names: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ # Defaulting to class default values if parameters are not provided if effect_modifier_names is None: effect_modifier_names = self._effect_modifier_names if num_quantiles is None: num_quantiles = self.num_quantiles_to_discretize_cont_cols # Checking that there is at least one effect modifier if not effect_modifier_names: raise ValueError("At least one effect modifier should be specified to compute conditional effects.") # Making sure that effect_modifier_names is a list effect_modifier_names = parse_state(effect_modifier_names) if not all(em in self._effect_modifier_names for em in effect_modifier_names): self.logger.warn( "At least one of the provided effect modifiers was not included while fitting the estimator. You may get incorrect results. To resolve, fit the estimator again by providing the updated effect modifiers in estimate_effect()." ) # Making a copy since we are going to be changing effect modifier names effect_modifier_names = effect_modifier_names.copy() prefix = CausalEstimator.TEMP_CAT_COLUMN_PREFIX # For every numeric effect modifier, adding a temp categorical column for i in range(len(effect_modifier_names)): em = effect_modifier_names[i] if pd.api.types.is_numeric_dtype(data[em].dtypes): data[prefix + str(em)] = pd.qcut(data[em], num_quantiles, duplicates="drop") effect_modifier_names[i] = prefix + str(em) # Grouping by effect modifiers and computing effect separately by_effect_mods = data.groupby(effect_modifier_names) cond_est_fn = lambda x: self._do(self._treatment_value, x) - self._do(self._control_value, x) conditional_estimates = by_effect_mods.apply(estimate_effect_fn) # Deleting the temporary categorical columns for em in effect_modifier_names: if em.startswith(prefix): data.pop(em) return conditional_estimates def _do(self, x, data_df=None): raise NotImplementedError( ("Do-operator is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG).format(self.__class__) ) def do(self, x, data_df=None): """Method that implements the do-operator. Given a value x for the treatment, returns the expected value of the outcome when the treatment is intervened to a value x. :param x: Value of the treatment :param data_df: Data on which the do-operator is to be applied. :returns: Value of the outcome when treatment is intervened/set to x. """ est = self._do(x, data_df) return est def construct_symbolic_estimator(self, estimand): raise NotImplementedError(("Symbolic estimator string is ").format(self.__class__)) def _generate_bootstrap_estimates(self, data: pd.DataFrame, num_bootstrap_simulations, sample_size_fraction): """Helper function to generate causal estimates over bootstrapped samples. :param num_bootstrap_simulations: Number of simulations for the bootstrap method. :param sample_size_fraction: Fraction of the dataset to be resampled. :returns: A collections.namedtuple containing a list of bootstrapped estimates and a dictionary containing parameters used for the bootstrap. """ # The array that stores the results of all estimations simulation_results = np.zeros(num_bootstrap_simulations) # Find the sample size the proportion with the population size sample_size = int(sample_size_fraction * len(data)) if sample_size > len(data): self.logger.warning("WARN: The sample size is greater than the data being sampled") self.logger.info("INFO: The sample size: {}".format(sample_size)) self.logger.info("INFO: The number of simulations: {}".format(num_bootstrap_simulations)) # Perform the set number of simulations for index in range(num_bootstrap_simulations): new_data = resample(data, n_samples=sample_size) new_estimator = self.get_new_estimator_object( self._target_estimand, # names of treatment and outcome test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, ) new_estimator.fit( new_data, effect_modifier_names=self._effect_modifier_names, ) new_effect = new_estimator.estimate_effect( new_data, treatment_value=self._treatment_value, control_value=self._control_value, target_units=self._target_units, ) simulation_results[index] = new_effect.value estimates = CausalEstimator.BootstrapEstimates( simulation_results, {"num_simulations": num_bootstrap_simulations, "sample_size_fraction": sample_size_fraction}, ) return estimates def _estimate_confidence_intervals_with_bootstrap( self, data: pd.DataFrame, estimate_value, confidence_level=None, num_simulations=None, sample_size_fraction=None, ): """ Method to compute confidence interval using bootstrapped sampling. :param estimate_value: obtained estimate's value :param confidence_level: The level for which to compute CI (e.g., 95% confidence level translates to confidence_level=0.95) :param num_simulations: The number of simulations to be performed to get the bootstrap confidence intervals. :param sample_size_fraction: The fraction of the dataset to be resampled. :returns: confidence interval at the specified level. For more details on bootstrap or resampling statistics, refer to the following links: https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading24.pdf https://projecteuclid.org/download/pdf_1/euclid.ss/1032280214 """ # Using class default parameters if not specified if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(data, num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Checked if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(data, num_simulations, sample_size_fraction) # Now use the data obtained from the simulations to get the value of the confidence estimates bootstrap_estimates = self._bootstrap_estimates.estimates # Get the variations of each bootstrap estimate and sort bootstrap_variations = [bootstrap_estimate - estimate_value for bootstrap_estimate in bootstrap_estimates] sorted_bootstrap_variations = np.sort(bootstrap_variations) # Now we take the (1- p)th and the (p)th variations, where p is the chosen confidence level upper_bound_index = int((1 - confidence_level) * len(sorted_bootstrap_variations)) lower_bound_index = int(confidence_level * len(sorted_bootstrap_variations)) # Get the lower and upper bounds by subtracting the variations from the estimate lower_bound = estimate_value - sorted_bootstrap_variations[lower_bound_index] upper_bound = estimate_value - sorted_bootstrap_variations[upper_bound_index] return lower_bound, upper_bound def _estimate_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a confidence interval estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating confidence intervals is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate confidence intervals." ).format(self.__class__) ) def estimate_confidence_intervals( self, data: pd.DataFrame, estimate_value, confidence_level=None, method=None, **kwargs ): """Find the confidence intervals corresponding to any estimator By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param estimate_value: obtained estimate's value :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals # this is either True or methodname else: method = "default" confidence_intervals = None if confidence_level is None: confidence_level = self.confidence_level if method == "default" or method is True: # user has not provided any method try: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) except NotImplementedError: confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( data, estimate_value, confidence_level, **kwargs ) else: if method == "bootstrap": confidence_intervals = self._estimate_confidence_intervals_with_bootstrap( data, estimate_value, confidence_level, **kwargs ) else: confidence_intervals = self._estimate_confidence_intervals(confidence_level, method=method, **kwargs) return confidence_intervals def _estimate_std_error_with_bootstrap(self, data: pd.DataFrame, num_simulations=None, sample_size_fraction=None): """Compute standard error using the bootstrap method. Standard error and confidence intervals use the same parameter num_simulations for the number of bootstrap simulations. :param num_simulations: Number of bootstrapped samples. :param sample_size_fraction: Fraction of data to be resampled. :returns: Standard error of the obtained estimate. """ # Use existing params, if new user defined params are not present if num_simulations is None: num_simulations = self.num_simulations if sample_size_fraction is None: sample_size_fraction = self.sample_size_fraction # Checking if bootstrap_estimates are already computed if self._bootstrap_estimates is None: self._bootstrap_estimates = self._generate_bootstrap_estimates(data, num_simulations, sample_size_fraction) elif CausalEstimator.is_bootstrap_parameter_changed(self._bootstrap_estimates.params, locals()): # Check if any parameter is changed from the previous std error estimate self._bootstrap_estimates = self._generate_bootstrap_estimates(data, num_simulations, sample_size_fraction) std_error = np.std(self._bootstrap_estimates.estimates) return std_error def _estimate_std_error(self, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a standard error estimation method suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for estimating standard errors is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to estimate standard errors." ).format(self.__class__) ) def estimate_std_error(self, data: pd.DataFrame, method=None, **kwargs): """Compute standard error of an obtained causal estimate. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ if method is None: if self._confidence_intervals: method = self._confidence_intervals else: method = "default" std_error = None if method == "default" or method is True: # user has not provided any method try: std_error = self._estimate_std_error(method, **kwargs) except NotImplementedError: std_error = self._estimate_std_error_with_bootstrap(data, **kwargs) else: if method == "bootstrap": std_error = self._estimate_std_error_with_bootstrap(data, **kwargs) else: std_error = self._estimate_std_error(method, **kwargs) return std_error def _test_significance_with_bootstrap(self, data: pd.DataFrame, estimate_value, num_null_simulations=None): """Test statistical significance of an estimate using the bootstrap method. :param estimate_value: Obtained estimate's value :param num_null_simulations: Number of simulations for the null hypothesis :returns: p-value of the statistical significance test. """ # Use existing params, if new user defined params are not present if num_null_simulations is None: num_null_simulations = self.num_null_simulations do_retest = self._bootstrap_null_estimates is None or CausalEstimator.is_bootstrap_parameter_changed( self._bootstrap_null_estimates.params, locals() ) if do_retest: null_estimates = np.zeros(num_null_simulations) for i in range(num_null_simulations): new_outcome = np.random.permutation(data[self._target_estimand.outcome_variable]) new_data = data.assign(dummy_outcome=new_outcome) # self._outcome = self._data["dummy_outcome"] new_estimator = self.get_new_estimator_object( self._target_estimand, test_significance=False, evaluate_effect_strength=False, confidence_intervals=False, ) new_estimator.fit( data=new_data, effect_modifier_names=self._effect_modifier_names, ) new_effect = new_estimator.estimate_effect( new_data, target_units=self._target_units, ) null_estimates[i] = new_effect.value self._bootstrap_null_estimates = CausalEstimator.BootstrapEstimates( null_estimates, {"num_null_simulations": num_null_simulations, "sample_size_fraction": 1} ) # Processing the null hypothesis estimates sorted_null_estimates = np.sort(self._bootstrap_null_estimates.estimates) self.logger.debug("Null estimates: {0}".format(sorted_null_estimates)) median_estimate = sorted_null_estimates[int(num_null_simulations / 2)] # Doing a two-sided test if estimate_value > median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="left") p_value = 1 - (estimate_index / num_null_simulations) if estimate_value <= median_estimate: # Being conservative with the p-value reported estimate_index = np.searchsorted(sorted_null_estimates, estimate_value, side="right") p_value = estimate_index / num_null_simulations # If the estimate_index is 0, it depends on the number of simulations if p_value == 0: p_value = (0, 1 / len(sorted_null_estimates)) # a tuple determining the range. elif p_value == 1: p_value = (1 - 1 / len(sorted_null_estimates), 1) signif_dict = {"p_value": p_value} return signif_dict def _test_significance(self, estimate_value, method=None, **kwargs): """ This method is to be overriden by the child classes, so that they can run a significance test suited to the specific causal estimator. """ raise NotImplementedError( ( "This method for testing statistical significance is " + CausalEstimator.DEFAULT_NOTIMPLEMENTEDERROR_MSG + " Meanwhile, you can try the bootstrap method (method='bootstrap') to test statistical significance." ).format(self.__class__) ) def test_significance(self, data: pd.DataFrame, estimate_value, method=None, **kwargs): """Test statistical significance of obtained estimate. By default, uses resampling to create a non-parametric significance test. A general procedure. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param self: object instance of class Estimator :param estimate_value: obtained estimate's value :param method: Method for checking statistical significance :returns: p-value from the significance test """ if method is None: if self._significance_test: method = self._significance_test # this is either True or methodname else: method = "default" signif_dict = None if method == "default" or method is True: # user has not provided any method try: signif_dict = self._test_significance(estimate_value, method, **kwargs) except NotImplementedError: signif_dict = self._test_significance_with_bootstrap(data, estimate_value, **kwargs) else: if method == "bootstrap": signif_dict = self._test_significance_with_bootstrap(data, estimate_value, **kwargs) else: signif_dict = self._test_significance(estimate_value, method, **kwargs) return signif_dict def evaluate_effect_strength(self, data: pd.DataFrame, estimate): fraction_effect_explained = self._evaluate_effect_strength(data, estimate, method="fraction-effect") # Need to test r-squared before supporting # effect_r_squared = self._evaluate_effect_strength(estimate, method="r-squared") strength_dict = { "fraction-effect": fraction_effect_explained # 'r-squared': effect_r_squared } return strength_dict def _evaluate_effect_strength(self, data: pd.DataFrame, estimate, method="fraction-effect"): supported_methods = ["fraction-effect"] if method not in supported_methods: raise NotImplementedError("This method is not supported for evaluating effect strength") if method == "fraction-effect": naive_obs_estimate = self.estimate_effect_naive(data) self.logger.debug(estimate.value, naive_obs_estimate.value) fraction_effect_explained = estimate.value / naive_obs_estimate.value return fraction_effect_explained # elif method == "r-squared": # outcome_mean = np.mean(self._outcome) # total_variance = np.sum(np.square(self._outcome - outcome_mean)) # Assuming a linear model with one variable: the treatment # Currently only works for continuous y # causal_model = outcome_mean + estimate.value*self._treatment # squared_residual = np.sum(np.square(self._outcome - causal_model)) # r_squared = 1 - (squared_residual/total_variance) # return r_squared else: return None def update_input(self, treatment_value, control_value, target_units): self._control_value = control_value self._treatment_value = treatment_value self._target_units = target_units @staticmethod def is_bootstrap_parameter_changed(bootstrap_estimates_params, given_params): """Check whether parameters of the bootstrap have changed. This is an efficiency method that checks if fresh resampling of the bootstrap samples is required. Returns True if parameters have changed and resampling should be done again. :param bootstrap_estimates_params: A dictionary of parameters for the current bootstrap samples :param given_params: A dictionary of parameters passed by the user :returns: A binary flag denoting whether the parameters are different. """ is_any_parameter_changed = False for prm, val in bootstrap_estimates_params.items(): given_val = given_params.get(prm, None) if given_val is not None and given_val != val: is_any_parameter_changed = True break return is_any_parameter_changed def target_units_tostr(self): s = "" if type(self._target_units) is str: s += self._target_units elif callable(self._target_units): s += "Data subset defined by a function" elif isinstance(self._target_units, pd.DataFrame): s += "Data subset provided as a data frame" return s def signif_results_tostr(self, signif_results): s = "" pval = signif_results["p_value"] if type(pval) is tuple: s += "[{0}, {1}]".format(pval[0], pval[1]) else: s += "{0}".format(pval) return s def estimate_effect( data: pd.DataFrame, treatment: Union[str, List[str]], outcome: Union[str, List[str]], identifier_name: str, estimator: CausalEstimator, control_value: int = 0, treatment_value: int = 1, target_units: str = "ate", effect_modifiers: List[str] = None, fit_estimator: bool = True, method_params: Optional[Dict] = None, ): """Estimate the identified causal effect. In addition, you can directly call any of the EconML estimation methods. The convention is "backdoor.econml.path-to-estimator-class". For example, for the double machine learning estimator ("DML" class) that is located inside "dml" module of EconML, you can use the method name, "backdoor.econml.dml.DML". CausalML estimators can also be called. See `this demo notebook <https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html>`_. :param treatment: Name of the treatment :param outcome: Name of the outcome :param identified_estimand: a probability expression that represents the effect to be estimated. Output of CausalModel.identify_effect method :param estimator: Instance of a CausalEstimator to use :param control_value: Value of the treatment in the control group, for effect estimation. If treatment is multi-variate, this can be a list. :param treatment_value: Value of the treatment in the treated group, for effect estimation. If treatment is multi-variate, this can be a list. :param target_units: (Experimental) The units for which the treatment effect should be estimated. This can be of three types. (1) a string for common specifications of target units (namely, "ate", "att" and "atc"), (2) a lambda function that can be used as an index for the data (pandas DataFrame), or (3) a new DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. :param effect_modifiers: Names of effect modifier variables can be (optionally) specified here too, since they do not affect identification. If None, the effect_modifiers from the CausalModel are used. :param fit_estimator: Boolean flag on whether to fit the estimator. Setting it to False is useful to estimate the effect on new data using a previously fitted estimator. :returns: An instance of the CausalEstimate class, containing the causal effect estimate and other method-dependent information """ if effect_modifiers is None: effect_modifiers = [] treatment = parse_state(treatment) outcome = parse_state(outcome) causal_estimator_class = estimator.__class__ identified_estimand = estimator._target_estimand identified_estimand.set_identifier_method(identifier_name) if identified_estimand.no_directed_path: logger.warning("No directed path from {0} to {1}.".format(treatment, outcome)) return CausalEstimate( None, None, None, 0, identified_estimand, None, control_value=control_value, treatment_value=treatment_value ) # Check if estimator's target estimand is identified elif identified_estimand.estimands[identifier_name] is None: logger.error("No valid identified estimand available.") return CausalEstimate( None, None, None, None, None, control_value=control_value, treatment_value=treatment_value ) if fit_estimator: estimator.fit( data=data, effect_modifier_names=effect_modifiers, **method_params["fit_params"] if "fit_params" in method_params else {}, ) estimate = estimator.estimate_effect( data, treatment_value=treatment_value, control_value=control_value, target_units=target_units, confidence_intervals=estimator._confidence_intervals, ) if estimator._significance_test: estimator.test_significance(data, estimate.value, method=estimator._significance_test) if estimator._confidence_intervals: estimator.estimate_confidence_intervals( data, estimate.value, confidence_level=estimator.confidence_level, method=estimator._confidence_intervals, ) if estimator._effect_strength_eval: effect_strength_dict = estimator.evaluate_effect_strength(data, estimate) estimate.add_effect_strength(effect_strength_dict) # Store parameters inside estimate object for refutation methods # TODO: This add_params needs to move to the estimator class # inside estimate_effect and estimate_conditional_effect estimate.add_params( estimand_type=identified_estimand.estimand_type, estimator_class=causal_estimator_class, test_significance=estimator._significance_test, evaluate_effect_strength=estimator._effect_strength_eval, confidence_intervals=estimator._confidence_intervals, target_units=target_units, effect_modifiers=effect_modifiers, ) return estimate class CausalEstimate: """Class for the estimate object that every causal estimator returns""" def __init__( self, data, treatment_name, outcome_name, estimate, target_estimand, realized_estimand_expr, control_value, treatment_value, conditional_estimates=None, **kwargs, ): # TODO: Remove _data, _treatment_name and _outcome_name from this object # we save them here to enable the methods that required these properties saved in the estimator # eventually we should call those methods and just save the results in this object # instead of having this object invoke the estimator methods with the data. self._data = data self._treatment_name = treatment_name self._outcome_name = outcome_name self.value = estimate self.target_estimand = target_estimand self.realized_estimand_expr = realized_estimand_expr self.control_value = control_value self.treatment_value = treatment_value self.conditional_estimates = conditional_estimates self.params = kwargs if self.params is not None: for key, value in self.params.items(): setattr(self, key, value) self.effect_strength = None def add_estimator(self, estimator_instance): self.estimator = estimator_instance def add_effect_strength(self, strength_dict): self.effect_strength = strength_dict def add_params(self, **kwargs): self.params.update(kwargs) def get_confidence_intervals(self, confidence_level=None, method=None, **kwargs): """Get confidence intervals of the obtained estimate. By default, this is done with the help of bootstrapped confidence intervals but can be overridden if the specific estimator implements other methods of estimating confidence intervals. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for estimating confidence intervals. :param confidence_level: The confidence level of the confidence intervals of the estimate. :param kwargs: Other optional args to be passed to the CI method. :returns: The obtained confidence interval. """ confidence_intervals = self.estimator.estimate_confidence_intervals( data=self._data, estimate_value=self.value, confidence_level=confidence_level, method=method, **kwargs, ) return confidence_intervals def get_standard_error(self, method=None, **kwargs): """Get standard error of the obtained estimate. By default, this is done with the help of bootstrapped standard errors but can be overridden if the specific estimator implements other methods of estimating standard error. If the method provided is not bootstrap, this function calls the implementation of the specific estimator. :param method: Method for computing the standard error. :param kwargs: Other optional parameters to be passed to the estimating method. :returns: Standard error of the causal estimate. """ std_error = self.estimator.estimate_std_error(self._data, method=method, **kwargs) return std_error def test_stat_significance(self, method=None, **kwargs): """Test statistical significance of the estimate obtained. By default, uses resampling to create a non-parametric significance test. Individual child estimators can implement different methods. If the method name is different from "bootstrap", this function calls the implementation of the child estimator. :param method: Method for checking statistical significance :param kwargs: Other optional parameters to be passed to the estimating method. :returns: p-value from the significance test """ signif_results = self.estimator.test_significance(self._data, self.value, method=method, **kwargs) return {"p_value": signif_results["p_value"]} def estimate_conditional_effects( self, effect_modifiers=None, num_quantiles=CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS ): """Estimate treatment effect conditioned on given variables. If a numeric effect modifier is provided, it is discretized into quantile bins. If you would like a custom discretization, you can do so yourself: create a new column containing the discretized effect modifier and then include that column's name in the effect_modifier_names argument. :param effect_modifiers: Names of effect modifier variables over which the conditional effects will be estimated. If not provided, defaults to the effect modifiers specified during creation of the CausalEstimator object. :param num_quantiles: The number of quantiles into which a numeric effect modifier variable is discretized. Does not affect any categorical effect modifiers. :returns: A (multi-index) dataframe that provides separate effects for each value of the (discretized) effect modifiers. """ return self.estimator._estimate_conditional_effects( self.estimator._estimate_effect_fn, effect_modifiers, num_quantiles ) def interpret(self, method_name=None, **kwargs): """Interpret the causal estimate. :param method_name: Method used (string) or a list of methods. If None, then the default for the specific estimator is used. :param kwargs:: Optional parameters that are directly passed to the interpreter method. :returns: None """ if method_name is None: method_name = self.estimator.interpret_method method_name_arr = parse_state(method_name) for method in method_name_arr: interpreter = interpreters.get_class_object(method) interpreter(self, **kwargs).interpret(self._data) def __str__(self): s = "*** Causal Estimate ***\n" # No estimand was identified (identification failed) if self.target_estimand is None: return "Estimation failed! No relevant identified estimand available for this estimation method." s += "\n## Identified estimand\n{0}".format(self.target_estimand.__str__(only_target_estimand=True)) s += "\n## Realized estimand\n{0}".format(self.realized_estimand_expr) if hasattr(self, "estimator"): s += "\nTarget units: {0}\n".format(self.estimator.target_units_tostr()) s += "\n## Estimate\n" s += "Mean value: {0}\n".format(self.value) s += "" if hasattr(self, "cate_estimates"): s += "Effect estimates: {0}\n".format(self.cate_estimates) if hasattr(self, "estimator"): if self.estimator._significance_test: s += "p-value: {0}\n".format( self.estimator.signif_results_tostr(self.test_stat_significance(self._data)) ) if self.estimator._confidence_intervals: s += "{0}% confidence interval: {1}\n".format( 100 * self.estimator.confidence_level, self.get_confidence_intervals(self._data) ) if self.conditional_estimates is not None: s += "### Conditional Estimates\n" s += str(self.conditional_estimates) if self.effect_strength is not None: s += "\n## Effect Strength\n" s += "Change in outcome attributable to treatment: {}\n".format(self.effect_strength["fraction-effect"]) # s += "Variance in outcome explained by treatment: {}\n".format(self.effect_strength["r-squared"]) return s class RealizedEstimand(object): def __init__(self, identified_estimand, estimator_name): self.treatment_variable = identified_estimand.treatment_variable self.outcome_variable = identified_estimand.outcome_variable self.backdoor_variables = identified_estimand.get_backdoor_variables() self.instrumental_variables = identified_estimand.instrumental_variables self.estimand_type = identified_estimand.estimand_type self.estimand_expression = None self.assumptions = None self.estimator_name = estimator_name def update_assumptions(self, estimator_assumptions): self.assumptions = estimator_assumptions def update_estimand_expression(self, estimand_expression): self.estimand_expression = estimand_expression def __str__(self): s = "Realized estimand: {0}\n".format(self.estimator_name) s += "Realized estimand type: {0}\n".format(self.estimand_type) s += "Estimand expression:\n{0}\n".format(sp.pretty(self.estimand_expression)) j = 1 for ass_name, ass_str in self.assumptions.items(): s += "Estimand assumption {0}, {1}: {2}\n".format(j, ass_name, ass_str) j += 1 return s

andresmor-ms

325cf4e245de3e55b85a42c5fefc36f6ef34db46

c3e1c75696a8297aa48977ea4c7b7e8dc50dc6aa

same comment, I suggest removing the treatment_name argument.

amit-sharma

py-why/dowhy

Enhancement/remove data from estimators

* Remove data, treatment and outcome from estimator object * estimate_effect now have data, treatment and outcome as parameters

2023-01-03 18:39:35+00:00

2023-01-20 11:06:39+00:00

dowhy/causal_estimators/econml.py

import inspect from importlib import import_module from typing import Any, Callable, List, Optional, Protocol, Union from warnings import warn import numpy as np import pandas as pd from numpy.distutils.misc_util import is_sequence from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_identifier import IdentifiedEstimand from dowhy.utils.api import parse_state class _EconmlEstimator(Protocol): def fit(self, *args, **kwargs): ... def effect(self, *args, **kwargs): ... def effect_interval(self, *args, **kwargs): ... def effect_inference(self, *args, **kwargs): ... def shap_values(self, *args, **kwargs): ... class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__( self, identified_estimand: IdentifiedEstimand, econml_estimator: Union[_EconmlEstimator, str], test_significance: bool = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """ :param identified_estimand: probability expression representing the target identified estimand to estimate. :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, econml_estimator=econml_estimator, **kwargs, ) if isinstance(econml_estimator, str): warn( "Using a string to specify the value for econml_estimator is now deprecated, please provide an instance of a econml object", DeprecationWarning, stacklevel=2, ) estimator_class = self._get_econml_class_object(econml_estimator) self.estimator = estimator_class(**kwargs["init_params"]) else: self.estimator = econml_estimator self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method def fit( self, data: pd.DataFrame, treatment_name: str, outcome_name: str, effect_modifier_names: Optional[List[str]] = None, **kwargs, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._set_data(data, treatment_name, outcome_name) self._set_effect_modifiers(effect_modifier_names) # Save parameters for later refutter fitting self._econml_fit_params = kwargs self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # Enforcing this ordering is necessary to feed through the propensity values from dataset self._observed_common_causes_names = [ c for c in self._observed_common_causes_names if "propensity" not in c ] + sorted([c for c in self._observed_common_causes_names if "propensity" in c]) # For metalearners only--issue a warning if w contains variables not in x if self.estimator.__module__.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + self.estimator.__class__.__name__ + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) X = None W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None and len(self._effect_modifiers) > 0: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } self.estimator.fit(**estimator_data_args, **kwargs) return self def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def estimate_effect( self, data: pd.DataFrame = None, treatment_value: Any = 1, control_value: Any = 0, target_units=None, **_ ): """ data: dataframe containing the data on which treatment effect is to be estimated. treatment_value: value of the treatment variable for which the effect is to be estimated. control_value: value of the treatment variable that denotes its absence (usually 0) target_units: The units for which the treatment effect should be estimated. It can be a DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. It can also be a lambda function that can be used as an index for the data (pandas DataFrame) to select the required rows. """ if data is None: data = self._data self._target_units = target_units self._treatment_value = treatment_value self._control_value = control_value n_samples = self._treatment.shape[0] X = None # Effect modifiers if self._effect_modifiers is not None and len(self._effect_modifiers) > 0: X = self._effect_modifiers X_test = X if X is not None: if type(target_units) is pd.DataFrame: X_test = target_units elif callable(target_units): filtered_rows = data.where(target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] # Changing shape to a list for a singleton value self._treatment_value = parse_state(self._treatment_value) est = self.effect(X_test) ate = np.mean(est, axis=0) # one value per treatment value if len(ate) == 1: ate = ate[0] if self._confidence_intervals: self.effect_intervals = self.effect_interval(X_test) else: self.effect_intervals = None estimate = CausalEstimate( estimate=ate, control_value=control_value, treatment_value=treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) estimate.add_estimator(self) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) if self.estimator.__module__.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def apply_multitreatment(self, df: pd.DataFrame, fun: Callable, *args, **kwargs): ests = [] assert not isinstance(self._treatment_value, str) assert is_sequence(self._treatment_value) if df is None: filtered_df = None else: filtered_df = df[self._effect_modifier_names].values for tv in self._treatment_value: ests.append( fun( filtered_df, T0=self._control_value, T1=tv, *args, **kwargs, ) ) est = np.stack(ests, axis=1) return est def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise estimated treatment effect, output shape n_units x n_treatment_values (not counting control) :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_fun, *args, **kwargs) def effect_interval(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise confidence intervals for the estimated treatment effect :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_interval_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_interval( filtered_df, T0=T0, T1=T1, alpha=1 - self.confidence_level, *args, **kwargs ) return self.apply_multitreatment(df, effect_interval_fun, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs): """ Inference (uncertainty) results produced by the underlying EconML estimator :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_inference_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_inference(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_inference_fun, *args, **kwargs) def effect_tt(self, df: pd.DataFrame, *args, **kwargs): """ Effect of the actual treatment that was applied to each unit ("effect of Treatment on the Treated") :param df: Features of the units to evaluate :param args: passed through to estimator.effect() :param kwargs: passed through to estimator.effect() """ eff = self.effect(df, *args, **kwargs).reshape((len(df), len(self._treatment_value))) out = np.zeros(len(df)) treatment_value = parse_state(self._treatment_value) treatment_name = parse_state(self._treatment_name)[0] eff = np.reshape(eff, (len(df), len(treatment_value))) # For each unit, return the estimated effect of the treatment value # that was actually applied to the unit for c, col in enumerate(treatment_value): out[df[treatment_name] == col] = eff[df[treatment_name] == col, c] return pd.Series(data=out, index=df.index)

import inspect from importlib import import_module from typing import Any, Callable, List, Optional, Protocol, Union from warnings import warn import numpy as np import pandas as pd from numpy.distutils.misc_util import is_sequence from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_identifier import IdentifiedEstimand from dowhy.utils.api import parse_state class _EconmlEstimator(Protocol): def fit(self, *args, **kwargs): ... def effect(self, *args, **kwargs): ... def effect_interval(self, *args, **kwargs): ... def effect_inference(self, *args, **kwargs): ... def shap_values(self, *args, **kwargs): ... class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__( self, identified_estimand: IdentifiedEstimand, econml_estimator: Union[_EconmlEstimator, str], test_significance: Union[bool, str] = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """ :param identified_estimand: probability expression representing the target identified estimand to estimate. :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, econml_estimator=econml_estimator, **kwargs, ) if isinstance(econml_estimator, str): warn( "Using a string to specify the value for econml_estimator is now deprecated, please provide an instance of a econml object", DeprecationWarning, stacklevel=2, ) estimator_class = self._get_econml_class_object(econml_estimator) self.estimator = estimator_class(**kwargs["init_params"]) else: self.estimator = econml_estimator self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method def fit( self, data: pd.DataFrame, effect_modifier_names: Optional[List[str]] = None, **kwargs, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._set_effect_modifiers(data, effect_modifier_names) # Save parameters for later refutter fitting self._econml_fit_params = kwargs self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # Enforcing this ordering is necessary to feed through the propensity values from dataset self._observed_common_causes_names = [ c for c in self._observed_common_causes_names if "propensity" not in c ] + sorted([c for c in self._observed_common_causes_names if "propensity" in c]) # For metalearners only--issue a warning if w contains variables not in x if self.estimator.__module__.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + self.estimator.__class__.__name__ + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) X = None W = None # common causes/ confounders Z = None # Instruments Y = data[self._target_estimand.outcome_variable[0]] T = data[self._target_estimand.treatment_variable] if self._effect_modifiers is not None and len(self._effect_modifiers) > 0: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } self.estimator.fit(**estimator_data_args, **kwargs) return self def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def estimate_effect( self, data: pd.DataFrame, treatment_value: Any = 1, control_value: Any = 0, target_units=None, **_, ): """ data: dataframe containing the data on which treatment effect is to be estimated. treatment_value: value of the treatment variable for which the effect is to be estimated. control_value: value of the treatment variable that denotes its absence (usually 0) target_units: The units for which the treatment effect should be estimated. It can be a DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. It can also be a lambda function that can be used as an index for the data (pandas DataFrame) to select the required rows. """ self._target_units = target_units self._treatment_value = treatment_value self._control_value = control_value X = None # Effect modifiers if self._effect_modifiers is not None and len(self._effect_modifiers) > 0: X = self._effect_modifiers X_test = X if X is not None: if type(target_units) is pd.DataFrame: X_test = target_units elif callable(target_units): filtered_rows = data.where(target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] # Changing shape to a list for a singleton value self._treatment_value = parse_state(self._treatment_value) est = self.effect(X_test) ate = np.mean(est, axis=0) # one value per treatment value if len(ate) == 1: ate = ate[0] if self._confidence_intervals: self.effect_intervals = self.effect_interval(X_test) else: self.effect_intervals = None estimate = CausalEstimate( data=data, treatment_name=self._target_estimand.treatment_variable, outcome_name=self._target_estimand.outcome_variable, estimate=ate, control_value=control_value, treatment_value=treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) estimate.add_estimator(self) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) if self.estimator.__module__.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def apply_multitreatment(self, df: pd.DataFrame, fun: Callable, *args, **kwargs): ests = [] assert not isinstance(self._treatment_value, str) assert is_sequence(self._treatment_value) if df is None: filtered_df = None else: filtered_df = df[self._effect_modifier_names].values for tv in self._treatment_value: ests.append( fun( filtered_df, T0=self._control_value, T1=tv, *args, **kwargs, ) ) est = np.stack(ests, axis=1) return est def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise estimated treatment effect, output shape n_units x n_treatment_values (not counting control) :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_fun, *args, **kwargs) def effect_interval(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise confidence intervals for the estimated treatment effect :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_interval_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_interval( filtered_df, T0=T0, T1=T1, alpha=1 - self.confidence_level, *args, **kwargs ) return self.apply_multitreatment(df, effect_interval_fun, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs): """ Inference (uncertainty) results produced by the underlying EconML estimator :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_inference_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_inference(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_inference_fun, *args, **kwargs) def effect_tt(self, df: pd.DataFrame, treatment_value, *args, **kwargs): """ Effect of the actual treatment that was applied to each unit ("effect of Treatment on the Treated") :param df: Features of the units to evaluate :param args: passed through to estimator.effect() :param kwargs: passed through to estimator.effect() """ eff = self.effect(df, *args, **kwargs).reshape((len(df), len(self._treatment_value))) out = np.zeros(len(df)) treatment_value = parse_state(treatment_value) eff = np.reshape(eff, (len(df), len(treatment_value))) # For each unit, return the estimated effect of the treatment value # that was actually applied to the unit for c, col in enumerate(treatment_value): out[df[self._target_estimand.treatment_variable[0]] == col] = eff[ df[self._target_estimand.treatment_variable[0]] == col, c ] return pd.Series(data=out, index=df.index)

andresmor-ms

325cf4e245de3e55b85a42c5fefc36f6ef34db46

c3e1c75696a8297aa48977ea4c7b7e8dc50dc6aa

we might not need treatment_name

amit-sharma

py-why/dowhy

Enhancement/remove data from estimators

* Remove data, treatment and outcome from estimator object * estimate_effect now have data, treatment and outcome as parameters

2023-01-03 18:39:35+00:00

2023-01-20 11:06:39+00:00

dowhy/causal_estimators/generalized_linear_model_estimator.py

import itertools from typing import Any, List, Optional, Union import pandas as pd import statsmodels.api as sm from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier import IdentifiedEstimand class GeneralizedLinearModelEstimator(RegressionEstimator): """Compute effect of treatment using a generalized linear model such as logistic regression. Implementation uses statsmodels.api.GLM. Needs an additional parameter, "glm_family" to be specified in method_params. The value of this parameter can be any valid statsmodels.api families object. For example, to use logistic regression, specify "glm_family" as statsmodels.api.families.Binomial(). """ def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: bool = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, glm_family: Optional[Any] = None, predict_score: bool = True, **kwargs, ): """For a list of args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param glm_family: statsmodels family for the generalized linear model. For example, use statsmodels.api.families.Binomial() for logistic regression or statsmodels.api.families.Poisson() for count data. :param predict_score: For models that have a binary output, whether to output the model's score or the binary output based on the score. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, glm_family=glm_family, predict_score=predict_score, **kwargs, ) self.logger.info("INFO: Using Generalized Linear Model Estimator") if glm_family is not None: self.family = glm_family else: raise ValueError( "Need to specify the family for the generalized linear model. Provide a 'glm_family' parameter in method_params, such as statsmodels.api.families.Binomial() for logistic regression." ) self.predict_score = predict_score def fit( self, data: pd.DataFrame, treatment_name: str, outcome_name: str, effect_modifier_names: Optional[List[str]] = None, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ return super().fit(data, treatment_name, outcome_name, effect_modifier_names=effect_modifier_names) def _build_model(self): features = self._build_features() model = sm.GLM(self._outcome, features, family=self.family).fit() return (features, model) def predict_fn(self, model, features): # Checking if Y is binary outcome_values = self._data[self._outcome_name].astype(int).unique() outcome_is_binary = all([v in [0, 1] for v in outcome_values]) if outcome_is_binary: if self.predict_score: return model.predict(features) else: return (model.predict(features) > 0.5).astype(int) else: return model.predict(features) def construct_symbolic_estimator(self, estimand): expr = "b: " + ",".join(estimand.outcome_variable) + "~" + "Sigmoid(" var_list = estimand.treatment_variable + estimand.get_backdoor_variables() expr += "+".join(var_list) if self._effect_modifier_names: interaction_terms = [ "{0}*{1}".format(x[0], x[1]) for x in itertools.product(estimand.treatment_variable, self._effect_modifier_names) ] expr += "+" + "+".join(interaction_terms) expr += ")" return expr

import itertools from typing import Any, List, Optional, Union import pandas as pd import statsmodels.api as sm from dowhy.causal_estimator import CausalEstimator from dowhy.causal_estimators.regression_estimator import RegressionEstimator from dowhy.causal_identifier import IdentifiedEstimand class GeneralizedLinearModelEstimator(RegressionEstimator): """Compute effect of treatment using a generalized linear model such as logistic regression. Implementation uses statsmodels.api.GLM. Needs an additional parameter, "glm_family" to be specified in method_params. The value of this parameter can be any valid statsmodels.api families object. For example, to use logistic regression, specify "glm_family" as statsmodels.api.families.Binomial(). """ def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: Union[bool, str] = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, glm_family: Optional[Any] = None, predict_score: bool = True, **kwargs, ): """For a list of args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param glm_family: statsmodels family for the generalized linear model. For example, use statsmodels.api.families.Binomial() for logistic regression or statsmodels.api.families.Poisson() for count data. :param predict_score: For models that have a binary output, whether to output the model's score or the binary output based on the score. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, glm_family=glm_family, predict_score=predict_score, **kwargs, ) self.logger.info("INFO: Using Generalized Linear Model Estimator") if glm_family is not None: self.family = glm_family else: raise ValueError( "Need to specify the family for the generalized linear model. Provide a 'glm_family' parameter in method_params, such as statsmodels.api.families.Binomial() for logistic regression." ) self.predict_score = predict_score def fit( self, data: pd.DataFrame, effect_modifier_names: Optional[List[str]] = None, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ return super().fit( data, effect_modifier_names=effect_modifier_names, ) def _build_model(self, data: pd.DataFrame): features = self._build_features(data) model = sm.GLM(data[self._target_estimand.outcome_variable], features, family=self.family).fit() return (features, model) def predict_fn(self, data: pd.DataFrame, model, features): # Checking if Y is binary outcome_values = data[self._target_estimand.outcome_variable[0]].astype(int).unique() outcome_is_binary = all([v in [0, 1] for v in outcome_values]) if outcome_is_binary: if self.predict_score: return model.predict(features) else: return (model.predict(features) > 0.5).astype(int) else: return model.predict(features) def construct_symbolic_estimator(self, estimand): expr = "b: " + ",".join(estimand.outcome_variable) + "~" + "Sigmoid(" var_list = estimand.treatment_variable + estimand.get_backdoor_variables() expr += "+".join(var_list) if self._effect_modifier_names: interaction_terms = [ "{0}*{1}".format(x[0], x[1]) for x in itertools.product(estimand.treatment_variable, self._effect_modifier_names) ] expr += "+" + "+".join(interaction_terms) expr += ")" return expr

andresmor-ms

325cf4e245de3e55b85a42c5fefc36f6ef34db46

c3e1c75696a8297aa48977ea4c7b7e8dc50dc6aa

treatment and outcome names can be avoided for predict_fn and _build_model.

amit-sharma

py-why/dowhy

Enhancement/remove data from estimators

* Remove data, treatment and outcome from estimator object * estimate_effect now have data, treatment and outcome as parameters

2023-01-03 18:39:35+00:00

2023-01-20 11:06:39+00:00

dowhy/causal_estimators/instrumental_variable_estimator.py

from typing import Any, Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp import sympy.stats as spstats from statsmodels.sandbox.regression.gmm import IV2SLS from dowhy.causal_estimator import CausalEstimate, CausalEstimator, RealizedEstimand from dowhy.causal_identifier import IdentifiedEstimand from dowhy.utils.api import parse_state class InstrumentalVariableEstimator(CausalEstimator): """Compute effect of treatment using the instrumental variables method. This is also a superclass that can be inherited by other specific methods. Supports additional parameters as listed below. """ def __init__( self, identified_estimand: IdentifiedEstimand, iv_instrument_name: Optional[Union[List, Dict, str]] = None, test_significance: bool = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """ :param identified_estimand: probability expression representing the target identified estimand to estimate. :param iv_instrument_name: Name of the specific instrumental variable to be used. Needs to be one of the IVs identified in the identification step. Default is to use all the IV variables from the identification step. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, iv_instrument_name=iv_instrument_name, **kwargs, ) self.iv_instrument_name = iv_instrument_name self.logger.info("INFO: Using Instrumental Variable Estimator") def fit( self, data: pd.DataFrame, treatment_name: str, outcome_name: str, effect_modifier_names: Optional[List[str]] = None, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._set_data(data, treatment_name, outcome_name) self._set_effect_modifiers(effect_modifier_names) self.estimating_instrument_names = self._target_estimand.instrumental_variables if self.iv_instrument_name is not None: self.estimating_instrument_names = parse_state(self.iv_instrument_name) self.logger.debug("Instrumental Variables used:" + ",".join(self.estimating_instrument_names)) if not self.estimating_instrument_names: raise ValueError("No valid instruments found. IV Method not applicable") if len(self.estimating_instrument_names) < len(self._treatment_name): # TODO move this to the identification step raise ValueError( "Number of instruments fewer than number of treatments. 2SLS requires at least as many instruments as treatments." ) self._estimating_instruments = self._data[self.estimating_instrument_names] self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) return self def estimate_effect( self, data: pd.DataFrame = None, treatment_value: Any = 1, control_value: Any = 0, target_units=None, **_ ): """ data: dataframe containing the data on which treatment effect is to be estimated. treatment_value: value of the treatment variable for which the effect is to be estimated. control_value: value of the treatment variable that denotes its absence (usually 0) target_units: The units for which the treatment effect should be estimated. It can be a DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. It can also be a lambda function that can be used as an index for the data (pandas DataFrame) to select the required rows. """ if data is None: data = self._data self._target_units = target_units self._treatment_value = treatment_value self._control_value = control_value if len(self.estimating_instrument_names) == 1 and len(self._treatment_name) == 1: instrument = self._estimating_instruments.iloc[:, 0] self.logger.debug("Instrument Variable values: {0}".format(instrument)) num_unique_values = len(np.unique(instrument)) instrument_is_binary = num_unique_values <= 2 if instrument_is_binary: # Obtain estimate by Wald Estimator y1_z = np.mean(self._outcome[instrument == 1]) y0_z = np.mean(self._outcome[instrument == 0]) x1_z = np.mean(self._treatment[self._treatment_name[0]][instrument == 1]) x0_z = np.mean(self._treatment[self._treatment_name[0]][instrument == 0]) num = y1_z - y0_z deno = x1_z - x0_z iv_est = num / deno else: # Obtain estimate by 2SLS estimator: Cov(y,z) / Cov(x,z) num_yz = np.cov(self._outcome, instrument)[0, 1] deno_xz = np.cov(self._treatment[self._treatment_name[0]], instrument)[0, 1] iv_est = num_yz / deno_xz else: # More than 1 instrument. Use 2sls. est_treatment = self._treatment.astype(np.float32) est_outcome = self._outcome.astype(np.float32) ivmodel = IV2SLS(est_outcome, est_treatment, self._estimating_instruments) reg_results = ivmodel.fit() self.logger.debug(reg_results.summary()) iv_est = sum( reg_results.params ) # the effect is the same for any treatment value (assume treatment goes from 0 to 1) estimate = CausalEstimate( estimate=iv_est, control_value=control_value, treatment_value=treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) estimate.add_estimator(self) return estimate def construct_symbolic_estimator(self, estimand): sym_outcome = spstats.Normal(",".join(estimand.outcome_variable), 0, 1) sym_treatment = spstats.Normal(",".join(estimand.treatment_variable), 0, 1) sym_instrument = sp.Symbol(",".join(self.estimating_instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation(sym_outcome_derivative) / sp.stats.Expectation(sym_treatment_derivative) estimator_assumptions = { "treatment_effect_homogeneity": ( "Each unit's treatment {0} is ".format(self._treatment_name) + "affected in the same way by common causes of " "{0} and {1}".format(self._treatment_name, self._outcome_name) ), "outcome_effect_homogeneity": ( "Each unit's outcome {0} is ".format(self._outcome_name) + "affected in the same way by common causes of " "{0} and {1}".format(self._treatment_name, self._outcome_name) ), } sym_assumptions = {**estimand.estimands["iv"]["assumptions"], **estimator_assumptions} symbolic_estimand = RealizedEstimand(estimand, estimator_name="Wald Estimator") symbolic_estimand.update_assumptions(sym_assumptions) symbolic_estimand.update_estimand_expression(sym_effect) return symbolic_estimand

from typing import Any, Dict, List, Optional, Union import numpy as np import pandas as pd import sympy as sp import sympy.stats as spstats from statsmodels.sandbox.regression.gmm import IV2SLS from dowhy.causal_estimator import CausalEstimate, CausalEstimator, RealizedEstimand from dowhy.causal_identifier import IdentifiedEstimand from dowhy.utils.api import parse_state class InstrumentalVariableEstimator(CausalEstimator): """Compute effect of treatment using the instrumental variables method. This is also a superclass that can be inherited by other specific methods. Supports additional parameters as listed below. """ def __init__( self, identified_estimand: IdentifiedEstimand, iv_instrument_name: Optional[Union[List, Dict, str]] = None, test_significance: Union[bool, str] = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """ :param identified_estimand: probability expression representing the target identified estimand to estimate. :param iv_instrument_name: Name of the specific instrumental variable to be used. Needs to be one of the IVs identified in the identification step. Default is to use all the IV variables from the identification step. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, iv_instrument_name=iv_instrument_name, **kwargs, ) self.iv_instrument_name = iv_instrument_name self.logger.info("INFO: Using Instrumental Variable Estimator") def fit( self, data: pd.DataFrame, effect_modifier_names: Optional[List[str]] = None, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._set_effect_modifiers(data, effect_modifier_names) self.estimating_instrument_names = self._target_estimand.instrumental_variables if self.iv_instrument_name is not None: self.estimating_instrument_names = parse_state(self.iv_instrument_name) self.logger.debug("Instrumental Variables used:" + ",".join(self.estimating_instrument_names)) if not self.estimating_instrument_names: raise ValueError("No valid instruments found. IV Method not applicable") if len(self.estimating_instrument_names) < len(self._target_estimand.treatment_variable): # TODO move this to the identification step raise ValueError( "Number of instruments fewer than number of treatments. 2SLS requires at least as many instruments as treatments." ) self._estimating_instruments = data[self.estimating_instrument_names] self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) return self def estimate_effect( self, data: pd.DataFrame, treatment_value: Any = 1, control_value: Any = 0, target_units=None, **_, ): """ data: dataframe containing the data on which treatment effect is to be estimated. treatment_value: value of the treatment variable for which the effect is to be estimated. control_value: value of the treatment variable that denotes its absence (usually 0) target_units: The units for which the treatment effect should be estimated. It can be a DataFrame that contains values of the effect_modifiers and effect will be estimated only for this new data. It can also be a lambda function that can be used as an index for the data (pandas DataFrame) to select the required rows. """ self._target_units = target_units self._treatment_value = treatment_value self._control_value = control_value if len(self.estimating_instrument_names) == 1 and len(self._target_estimand.treatment_variable) == 1: instrument = self._estimating_instruments.iloc[:, 0] self.logger.debug("Instrument Variable values: {0}".format(instrument)) num_unique_values = len(np.unique(instrument)) instrument_is_binary = num_unique_values <= 2 if instrument_is_binary: # Obtain estimate by Wald Estimator y1_z = np.mean(data[self._target_estimand.outcome_variable[0]][instrument == 1]) y0_z = np.mean(data[self._target_estimand.outcome_variable[0]][instrument == 0]) x1_z = np.mean(data[self._target_estimand.treatment_variable[0]][instrument == 1]) x0_z = np.mean(data[self._target_estimand.treatment_variable[0]][instrument == 0]) num = y1_z - y0_z deno = x1_z - x0_z iv_est = num / deno else: # Obtain estimate by 2SLS estimator: Cov(y,z) / Cov(x,z) num_yz = np.cov(data[self._target_estimand.outcome_variable[0]], instrument)[0, 1] deno_xz = np.cov(data[self._target_estimand.treatment_variable[0]], instrument)[0, 1] iv_est = num_yz / deno_xz else: # More than 1 instrument. Use 2sls. est_treatment = data[self._target_estimand.treatment_variable].astype(np.float32) est_outcome = data[self._target_estimand.outcome_variable[0]].astype(np.float32) ivmodel = IV2SLS(est_outcome, est_treatment, self._estimating_instruments) reg_results = ivmodel.fit() self.logger.debug(reg_results.summary()) iv_est = sum( reg_results.params ) # the effect is the same for any treatment value (assume treatment goes from 0 to 1) estimate = CausalEstimate( data=data, treatment_name=self._target_estimand.treatment_variable, outcome_name=self._target_estimand.outcome_variable, estimate=iv_est, control_value=control_value, treatment_value=treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) estimate.add_estimator(self) return estimate def construct_symbolic_estimator(self, estimand): sym_outcome = spstats.Normal(",".join(estimand.outcome_variable), 0, 1) sym_treatment = spstats.Normal(",".join(estimand.treatment_variable), 0, 1) sym_instrument = sp.Symbol(",".join(self.estimating_instrument_names)) sym_outcome_derivative = sp.Derivative(sym_outcome, sym_instrument) sym_treatment_derivative = sp.Derivative(sym_treatment, sym_instrument) sym_effect = spstats.Expectation(sym_outcome_derivative) / sp.stats.Expectation(sym_treatment_derivative) estimator_assumptions = { "treatment_effect_homogeneity": ( "Each unit's treatment {0} is ".format(self._target_estimand.treatment_variable) + "affected in the same way by common causes of " "{0} and {1}".format(self._target_estimand.treatment_variable, self._target_estimand.outcome_variable) ), "outcome_effect_homogeneity": ( "Each unit's outcome {0} is ".format(self._target_estimand.outcome_variable) + "affected in the same way by common causes of " "{0} and {1}".format(self._target_estimand.treatment_variable, self._target_estimand.outcome_variable) ), } sym_assumptions = {**estimand.estimands["iv"]["assumptions"], **estimator_assumptions} symbolic_estimand = RealizedEstimand(estimand, estimator_name="Wald Estimator") symbolic_estimand.update_assumptions(sym_assumptions) symbolic_estimand.update_estimand_expression(sym_effect) return symbolic_estimand

andresmor-ms

325cf4e245de3e55b85a42c5fefc36f6ef34db46

c3e1c75696a8297aa48977ea4c7b7e8dc50dc6aa

can avoid treatment_name and outcome_name here too

amit-sharma

py-why/dowhy

Enhancement/remove data from estimators

* Remove data, treatment and outcome from estimator object * estimate_effect now have data, treatment and outcome as parameters

2023-01-03 18:39:35+00:00

2023-01-20 11:06:39+00:00

dowhy/causal_estimators/regression_estimator.py

from typing import Any, List, Optional, Union import numpy as np import pandas as pd import statsmodels.api as sm from dowhy.causal_estimator import CausalEstimate, CausalEstimator, IdentifiedEstimand class RegressionEstimator(CausalEstimator): """Compute effect of treatment using some regression function. Fits a regression model for estimating the outcome using treatment(s) and confounders. Base class for all regression models, inherited by LinearRegressionEstimator and GeneralizedLinearModelEstimator. """ def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: bool = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """ :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, **kwargs, ) self.model = None def fit( self, data: pd.DataFrame, treatment_name: str, outcome_name: str, effect_modifier_names: Optional[List[str]] = None, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._set_data(data, treatment_name, outcome_name) self._set_effect_modifiers(effect_modifier_names) self.logger.debug("Back-door variables used:" + ",".join(self._target_estimand.get_backdoor_variables())) self._observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(self._observed_common_causes_names) > 0: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) # The model is always built on the entire data _, self.model = self._build_model() coefficients = self.model.params[1:] # first coefficient is the intercept self.logger.debug("Coefficients of the fitted model: " + ",".join(map(str, coefficients))) self.logger.debug(self.model.summary()) return self def estimate_effect( self, data: pd.DataFrame = None, treatment_value: Any = 1, control_value: Any = 0, target_units=None, need_conditional_estimates=None, **_, ): if data is None: data = self._data self._target_units = target_units self._treatment_value = treatment_value self._control_value = control_value # TODO make treatment_value and control value also as local parameters # All treatments are set to the same constant value effect_estimate = self._do(treatment_value, data) - self._do(control_value, data) conditional_effect_estimates = None if need_conditional_estimates: conditional_effect_estimates = self._estimate_conditional_effects( self._estimate_effect_fn, effect_modifier_names=self._effect_modifier_names ) intercept_parameter = self.model.params[0] estimate = CausalEstimate( estimate=effect_estimate, control_value=control_value, treatment_value=treatment_value, conditional_estimates=conditional_effect_estimates, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, intercept=intercept_parameter, ) estimate.add_estimator(self) return estimate def _estimate_effect_fn(self, data_df): est = self.estimate_effect(data=data_df, need_conditional_estimates=False) return est.value def _build_features(self, treatment_values=None, data_df=None): # Using all data by default if data_df is None: data_df = self._data treatment_vals = pd.get_dummies(self._treatment, drop_first=True) observed_common_causes_vals = self._observed_common_causes effect_modifiers_vals = self._effect_modifiers else: treatment_vals = pd.get_dummies(data_df[self._treatment_name], drop_first=True) if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) # Fixing treatment value to the specified value, if provided if treatment_values is not None: treatment_vals = treatment_values if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() # treatment_vals and data_df should have same number of rows if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_treatment_cols = 1 if len(treatment_vals.shape) == 1 else treatment_vals.shape[1] n_samples = treatment_vals.shape[0] treatment_2d = treatment_vals.reshape((n_samples, n_treatment_cols)) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables features = sm.add_constant(features, has_constant="add") # to add an intercept term return features def _do(self, treatment_val, data_df=None): if data_df is None: data_df = self._data if not self.model: # The model is always built on the entire data _, self.model = self._build_model() # Replacing treatment values by given x # First, create interventional tensor in original space interventional_treatment_values = np.full((data_df.shape[0], len(self._treatment_name)), treatment_val) # Then, use pandas to ensure that the dummies are assigned correctly for a categorical treatment interventional_treatment_2d = pd.concat( [ self._treatment.copy(), pd.DataFrame(data=interventional_treatment_values, columns=self._treatment.columns), ], axis=0, ).astype(self._treatment.dtypes, copy=False) interventional_treatment_2d = pd.get_dummies(interventional_treatment_2d, drop_first=True) interventional_treatment_2d = interventional_treatment_2d[self._treatment.shape[0] :] new_features = self._build_features(treatment_values=interventional_treatment_2d, data_df=data_df) interventional_outcomes = self.predict_fn(self.model, new_features) return interventional_outcomes.mean()

from typing import Any, List, Optional, Union import numpy as np import pandas as pd import statsmodels.api as sm from dowhy.causal_estimator import CausalEstimate, CausalEstimator, IdentifiedEstimand class RegressionEstimator(CausalEstimator): """Compute effect of treatment using some regression function. Fits a regression model for estimating the outcome using treatment(s) and confounders. Base class for all regression models, inherited by LinearRegressionEstimator and GeneralizedLinearModelEstimator. """ def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: Union[bool, str] = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, **kwargs, ): """ :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, **kwargs, ) self.model = None def fit( self, data: pd.DataFrame, effect_modifier_names: Optional[List[str]] = None, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._set_effect_modifiers(data, effect_modifier_names) self.logger.debug("Back-door variables used:" + ",".join(self._target_estimand.get_backdoor_variables())) self._observed_common_causes_names = self._target_estimand.get_backdoor_variables() if len(self._observed_common_causes_names) > 0: self._observed_common_causes = data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) # The model is always built on the entire data _, self.model = self._build_model(data) coefficients = self.model.params[1:] # first coefficient is the intercept self.logger.debug("Coefficients of the fitted model: " + ",".join(map(str, coefficients))) self.logger.debug(self.model.summary()) return self def estimate_effect( self, data: pd.DataFrame, treatment_value: Any = 1, control_value: Any = 0, target_units=None, need_conditional_estimates=None, **_, ): self._target_units = target_units self._treatment_value = treatment_value self._control_value = control_value # TODO make treatment_value and control value also as local parameters # All treatments are set to the same constant value effect_estimate = self._do(data, treatment_value) - self._do(data, control_value) conditional_effect_estimates = None if need_conditional_estimates: conditional_effect_estimates = self._estimate_conditional_effects( data, self._estimate_effect_fn, effect_modifier_names=self._effect_modifier_names ) intercept_parameter = self.model.params[0] estimate = CausalEstimate( data=data, treatment_name=self._target_estimand.treatment_variable, outcome_name=self._target_estimand.outcome_variable, estimate=effect_estimate, control_value=control_value, treatment_value=treatment_value, conditional_estimates=conditional_effect_estimates, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, intercept=intercept_parameter, ) estimate.add_estimator(self) return estimate def _estimate_effect_fn(self, data_df): est = self.estimate_effect(data=data_df, need_conditional_estimates=False) return est.value def _build_features(self, data_df: pd.DataFrame, treatment_values=None): treatment_vals = pd.get_dummies(data_df[self._target_estimand.treatment_variable], drop_first=True) if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) # Fixing treatment value to the specified value, if provided if treatment_values is not None: treatment_vals = treatment_values if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() # treatment_vals and data_df should have same number of rows if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_treatment_cols = 1 if len(treatment_vals.shape) == 1 else treatment_vals.shape[1] n_samples = treatment_vals.shape[0] treatment_2d = treatment_vals.reshape((n_samples, n_treatment_cols)) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables features = sm.add_constant(features, has_constant="add") # to add an intercept term return features def _do(self, data_df: pd.DataFrame, treatment_val): if data_df is None: data_df = self._data if not self.model: # The model is always built on the entire data _, self.model = self._build_model(data_df) # Replacing treatment values by given x # First, create interventional tensor in original space interventional_treatment_values = np.full( (data_df.shape[0], len(self._target_estimand.treatment_variable)), treatment_val ) # Then, use pandas to ensure that the dummies are assigned correctly for a categorical treatment interventional_treatment_2d = pd.concat( [ data_df[self._target_estimand.treatment_variable].copy(), pd.DataFrame( data=interventional_treatment_values, columns=data_df[self._target_estimand.treatment_variable].columns, ), ], axis=0, ).astype(data_df[self._target_estimand.treatment_variable].dtypes, copy=False) interventional_treatment_2d = pd.get_dummies(interventional_treatment_2d, drop_first=True) interventional_treatment_2d = interventional_treatment_2d[ data_df[self._target_estimand.treatment_variable].shape[0] : ] new_features = self._build_features(data_df, treatment_values=interventional_treatment_2d) interventional_outcomes = self.predict_fn(data_df, self.model, new_features) return interventional_outcomes.mean()

andresmor-ms

325cf4e245de3e55b85a42c5fefc36f6ef34db46

c3e1c75696a8297aa48977ea4c7b7e8dc50dc6aa

treatment_name can be avoided here too as a parameter

amit-sharma

py-why/dowhy

Enhancement/remove data from estimators

* Remove data, treatment and outcome from estimator object * estimate_effect now have data, treatment and outcome as parameters

2023-01-03 18:39:35+00:00

2023-01-20 11:06:39+00:00

dowhy/causal_estimators/two_stage_regression_estimator.py

import copy from typing import Any, List, Optional, Type, Union import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_identifier import EstimandType, IdentifiedEstimand from dowhy.utils.api import parse_state class TwoStageRegressionEstimator(CausalEstimator): """Compute treatment effect whenever the effect is fully mediated by another variable (front-door) or when there is an instrument available. Currently only supports a linear model for the effects. Supports additional parameters as listed below. """ # First stage statistical model DEFAULT_FIRST_STAGE_MODEL = LinearRegressionEstimator # Second stage statistical model DEFAULT_SECOND_STAGE_MODEL = LinearRegressionEstimator def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: bool = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, first_stage_model: Optional[Union[CausalEstimator, Type[CausalEstimator]]] = None, second_stage_model: Optional[Union[CausalEstimator, Type[CausalEstimator]]] = None, **kwargs, ): """ :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param first_stage_model: First stage estimator to be used. Default is linear regression. :param second_stage_model: Second stage estimator to be used. Default is linear regression. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, first_stage_model=first_stage_model, second_stage_model=second_stage_model, **kwargs, ) self.logger.info("INFO: Using Two Stage Regression Estimator") # Check if the treatment is one-dimensional modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_first_stage_confounders if first_stage_model is not None: self._first_stage_model = ( first_stage_model if isinstance(first_stage_model, CausalEstimator) else first_stage_model( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) ) else: self._first_stage_model = self.__class__.DEFAULT_FIRST_STAGE_MODEL( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) self.logger.warning("First stage model not provided. Defaulting to sklearn.linear_model.LinearRegression.") modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_second_stage_confounders if second_stage_model is not None: self._second_stage_model = ( second_stage_model if isinstance(second_stage_model, CausalEstimator) else second_stage_model( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) ) else: modified_target_estimand = copy.deepcopy(self._target_estimand) self._second_stage_model = self.__class__.DEFAULT_SECOND_STAGE_MODEL( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) self.logger.warning("Second stage model not provided. Defaulting to backdoor.linear_regression.") if self._target_estimand.estimand_type == EstimandType.NONPARAMETRIC_NDE: modified_target_estimand.identifier_method = "backdoor" modified_target_estimand = copy.deepcopy(self._target_estimand) self._second_stage_model_nde = type(self._second_stage_model)( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) def fit( self, data: pd.DataFrame, treatment_name: str, outcome_name: str, effect_modifier_names: Optional[List[str]] = None, **_, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param iv_instrument_name: Name of the specific instrumental variable to be used. Needs to be one of the IVs identified in the identification step. Default is to use all the IV variables from the identification step. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._set_data(data, treatment_name, outcome_name) self._set_effect_modifiers(effect_modifier_names) if len(self._treatment_name) > 1: error_msg = str(self.__class__) + "cannot handle more than one treatment variable" raise Exception(error_msg) if self._target_estimand.identifier_method == "frontdoor": self.logger.debug("Front-door variable used:" + ",".join(self._target_estimand.get_frontdoor_variables())) self._frontdoor_variables_names = self._target_estimand.get_frontdoor_variables() if self._frontdoor_variables_names: self._frontdoor_variables = self._data[self._frontdoor_variables_names] else: self._frontdoor_variables = None error_msg = "No front-door variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "mediation": self.logger.debug("Mediators used:" + ",".join(self._target_estimand.get_mediator_variables())) self._mediators_names = self._target_estimand.get_mediator_variables() if self._mediators_names: self._mediators = self._data[self._mediators_names] else: self._mediators = None error_msg = "No mediator variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "iv": self.logger.debug( "Instrumental variables used:" + ",".join(self._target_estimand.get_instrumental_variables()) ) self._instrumental_variables_names = self._target_estimand.get_instrumental_variables() if self._instrumental_variables_names: self._instrumental_variables = self._data[self._instrumental_variables_names] else: self._instrumental_variables = None error_msg = "No instrumental variable present. Two stage regression is not applicable" self.logger.error(error_msg) if self._target_estimand.identifier_method == "frontdoor": self._first_stage_model._target_estimand.outcome_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": self._first_stage_model._target_estimand.outcome_variable = parse_state(self._mediators_names) self._first_stage_model.fit( data, treatment_name, parse_state(self._first_stage_model._target_estimand.outcome_variable), effect_modifier_names=effect_modifier_names, ) if self._target_estimand.identifier_method == "frontdoor": self._second_stage_model._target_estimand.treatment_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": self._second_stage_model._target_estimand.treatment_variable = parse_state(self._mediators_names) self._second_stage_model.fit( data, parse_state(self._second_stage_model._target_estimand.treatment_variable), parse_state(self._outcome_name), # to convert it to array before passing to causal estimator) effect_modifier_names=effect_modifier_names, ) if self._target_estimand.estimand_type == EstimandType.NONPARAMETRIC_NDE: self._second_stage_model_nde._target_estimand.identifier_method = "backdoor" self._second_stage_model_nde.fit( data, self._treatment_name, parse_state(self._outcome_name), # to convert it to array before passing to causal estimator) effect_modifier_names=effect_modifier_names, ) return self def estimate_effect( self, data: pd.DataFrame = None, treatment_value: Any = 1, control_value: Any = 0, target_units=None, **_ ): if data is None: data = self._data self._target_units = target_units self._treatment_value = treatment_value self._control_value = control_value estimate_value = None # First stage first_stage_estimate = self._first_stage_model.estimate_effect( control_value=control_value, treatment_value=treatment_value, target_units=target_units, ) # Second Stage second_stage_estimate = self._second_stage_model.estimate_effect( control_value=control_value, treatment_value=treatment_value, target_units=target_units, ) # Combining the two estimates natural_indirect_effect = first_stage_estimate.value * second_stage_estimate.value # This same estimate is valid for frontdoor as well as mediation (NIE) estimate_value = natural_indirect_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, estimand_type=EstimandType.NONPARAMETRIC_NIE, ) if self._target_estimand.estimand_type == EstimandType.NONPARAMETRIC_NDE: total_effect_estimate = self._second_stage_model_nde.estimate_effect( control_value=control_value, treatment_value=treatment_value, target_units=target_units ) natural_direct_effect = total_effect_estimate.value - natural_indirect_effect estimate_value = natural_direct_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, total_effect_estimate.realized_estimand_expr, estimand_type=self._target_estimand.estimand_type, ) estimate = CausalEstimate( estimate=estimate_value, control_value=control_value, treatment_value=treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) estimate.add_estimator(self) return estimate def build_first_stage_features(self): data_df = self._data treatment_vals = data_df[self._treatment_name] if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_samples = treatment_vals.shape[0] self.logger.debug("Number of samples" + str(n_samples) + str(len(self._treatment_name))) treatment_2d = treatment_vals.reshape((n_samples, len(self._treatment_name))) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables # features = sm.add_constant(features, has_constant='add') # to add an intercept term return features def construct_symbolic_estimator( self, first_stage_symbolic, second_stage_symbolic, total_effect_symbolic=None, estimand_type=None ): nie_symbolic = "(" + first_stage_symbolic + ")*(" + second_stage_symbolic + ")" if estimand_type == EstimandType.NONPARAMETRIC_NIE: return nie_symbolic elif estimand_type == EstimandType.NONPARAMETRIC_NDE: return "(" + total_effect_symbolic + ") - (" + nie_symbolic + ")"

import copy from typing import Any, List, Optional, Type, Union import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator from dowhy.causal_identifier import EstimandType, IdentifiedEstimand from dowhy.utils.api import parse_state class TwoStageRegressionEstimator(CausalEstimator): """Compute treatment effect whenever the effect is fully mediated by another variable (front-door) or when there is an instrument available. Currently only supports a linear model for the effects. Supports additional parameters as listed below. """ # First stage statistical model DEFAULT_FIRST_STAGE_MODEL = LinearRegressionEstimator # Second stage statistical model DEFAULT_SECOND_STAGE_MODEL = LinearRegressionEstimator def __init__( self, identified_estimand: IdentifiedEstimand, test_significance: Union[bool, str] = False, evaluate_effect_strength: bool = False, confidence_intervals: bool = False, num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST, num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI, sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION, confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL, need_conditional_estimates: Union[bool, str] = "auto", num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS, first_stage_model: Optional[Union[CausalEstimator, Type[CausalEstimator]]] = None, second_stage_model: Optional[Union[CausalEstimator, Type[CausalEstimator]]] = None, **kwargs, ): """ :param identified_estimand: probability expression representing the target identified estimand to estimate. :param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap. :param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect :param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap :param num_null_simulations: The number of simulations for testing the statistical significance of the estimator :param num_simulations: The number of simulations for finding the confidence interval (and/or standard error) for a estimate :param sample_size_fraction: The size of the sample for the bootstrap estimator :param confidence_level: The confidence level of the confidence interval estimate :param need_conditional_estimates: Boolean flag indicating whether conditional estimates should be computed. Defaults to True if there are effect modifiers in the graph :param num_quantiles_to_discretize_cont_cols: The number of quantiles into which a numeric effect modifier is split, to enable estimation of conditional treatment effect over it. :param first_stage_model: First stage estimator to be used. Default is linear regression. :param second_stage_model: Second stage estimator to be used. Default is linear regression. :param kwargs: (optional) Additional estimator-specific parameters """ super().__init__( identified_estimand=identified_estimand, test_significance=test_significance, evaluate_effect_strength=evaluate_effect_strength, confidence_intervals=confidence_intervals, num_null_simulations=num_null_simulations, num_simulations=num_simulations, sample_size_fraction=sample_size_fraction, confidence_level=confidence_level, need_conditional_estimates=need_conditional_estimates, num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols, first_stage_model=first_stage_model, second_stage_model=second_stage_model, **kwargs, ) self.logger.info("INFO: Using Two Stage Regression Estimator") # Check if the treatment is one-dimensional modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_first_stage_confounders if first_stage_model is not None: self._first_stage_model = ( first_stage_model if isinstance(first_stage_model, CausalEstimator) else first_stage_model( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) ) else: self._first_stage_model = self.__class__.DEFAULT_FIRST_STAGE_MODEL( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) self.logger.warning("First stage model not provided. Defaulting to sklearn.linear_model.LinearRegression.") modified_target_estimand = copy.deepcopy(self._target_estimand) modified_target_estimand.identifier_method = "backdoor" modified_target_estimand.backdoor_variables = self._target_estimand.mediation_second_stage_confounders if second_stage_model is not None: self._second_stage_model = ( second_stage_model if isinstance(second_stage_model, CausalEstimator) else second_stage_model( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) ) else: modified_target_estimand = copy.deepcopy(self._target_estimand) self._second_stage_model = self.__class__.DEFAULT_SECOND_STAGE_MODEL( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) self.logger.warning("Second stage model not provided. Defaulting to backdoor.linear_regression.") if self._target_estimand.estimand_type == EstimandType.NONPARAMETRIC_NDE: modified_target_estimand.identifier_method = "backdoor" modified_target_estimand = copy.deepcopy(self._target_estimand) self._second_stage_model_nde = type(self._second_stage_model)( modified_target_estimand, test_significance=self._significance_test, evaluate_effect_strength=self._effect_strength_eval, confidence_intervals=self._confidence_intervals, **kwargs, ) def fit( self, data: pd.DataFrame, effect_modifier_names: Optional[List[str]] = None, **_, ): """ Fits the estimator with data for effect estimation :param data: data frame containing the data :param treatment: name of the treatment variable :param outcome: name of the outcome variable :param iv_instrument_name: Name of the specific instrumental variable to be used. Needs to be one of the IVs identified in the identification step. Default is to use all the IV variables from the identification step. :param effect_modifiers: Variables on which to compute separate effects, or return a heterogeneous effect function. Not all methods support this currently. """ self._set_effect_modifiers(data, effect_modifier_names) if len(self._target_estimand.treatment_variable) > 1: error_msg = str(self.__class__) + "cannot handle more than one treatment variable" raise Exception(error_msg) if self._target_estimand.identifier_method == "frontdoor": self.logger.debug("Front-door variable used:" + ",".join(self._target_estimand.get_frontdoor_variables())) self._frontdoor_variables_names = self._target_estimand.get_frontdoor_variables() if self._frontdoor_variables_names: self._frontdoor_variables = data[self._frontdoor_variables_names] else: self._frontdoor_variables = None error_msg = "No front-door variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "mediation": self.logger.debug("Mediators used:" + ",".join(self._target_estimand.get_mediator_variables())) self._mediators_names = self._target_estimand.get_mediator_variables() if self._mediators_names: self._mediators = data[self._mediators_names] else: self._mediators = None error_msg = "No mediator variable present. Two stage regression is not applicable" self.logger.error(error_msg) elif self._target_estimand.identifier_method == "iv": self.logger.debug( "Instrumental variables used:" + ",".join(self._target_estimand.get_instrumental_variables()) ) self._instrumental_variables_names = self._target_estimand.get_instrumental_variables() if self._instrumental_variables_names: self._instrumental_variables = data[self._instrumental_variables_names] else: self._instrumental_variables = None error_msg = "No instrumental variable present. Two stage regression is not applicable" self.logger.error(error_msg) if self._target_estimand.identifier_method == "frontdoor": self._first_stage_model._target_estimand.outcome_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": self._first_stage_model._target_estimand.outcome_variable = parse_state(self._mediators_names) self._first_stage_model.fit( data, effect_modifier_names=effect_modifier_names, ) if self._target_estimand.identifier_method == "frontdoor": self._second_stage_model._target_estimand.treatment_variable = parse_state(self._frontdoor_variables_names) elif self._target_estimand.identifier_method == "mediation": self._second_stage_model._target_estimand.treatment_variable = parse_state(self._mediators_names) self._second_stage_model.fit( data, effect_modifier_names=effect_modifier_names, ) if self._target_estimand.estimand_type == EstimandType.NONPARAMETRIC_NDE: self._second_stage_model_nde._target_estimand.identifier_method = "backdoor" self._second_stage_model_nde.fit( data, effect_modifier_names=effect_modifier_names, ) return self def estimate_effect( self, data: pd.DataFrame, treatment_value: Any = 1, control_value: Any = 0, target_units=None, **_, ): self._target_units = target_units self._treatment_value = treatment_value self._control_value = control_value estimate_value = None # First stage first_stage_estimate = self._first_stage_model.estimate_effect( data, control_value=control_value, treatment_value=treatment_value, target_units=target_units, ) # Second Stage second_stage_estimate = self._second_stage_model.estimate_effect( data, control_value=control_value, treatment_value=treatment_value, target_units=target_units, ) # Combining the two estimates natural_indirect_effect = first_stage_estimate.value * second_stage_estimate.value # This same estimate is valid for frontdoor as well as mediation (NIE) estimate_value = natural_indirect_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, estimand_type=EstimandType.NONPARAMETRIC_NIE, ) if self._target_estimand.estimand_type == EstimandType.NONPARAMETRIC_NDE: total_effect_estimate = self._second_stage_model_nde.estimate_effect( data, control_value=control_value, treatment_value=treatment_value, target_units=target_units, ) natural_direct_effect = total_effect_estimate.value - natural_indirect_effect estimate_value = natural_direct_effect self.symbolic_estimator = self.construct_symbolic_estimator( first_stage_estimate.realized_estimand_expr, second_stage_estimate.realized_estimand_expr, total_effect_estimate.realized_estimand_expr, estimand_type=self._target_estimand.estimand_type, ) estimate = CausalEstimate( data=data, treatment_name=self._target_estimand.treatment_variable, outcome_name=self._target_estimand.outcome_variable, estimate=estimate_value, control_value=control_value, treatment_value=treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, ) estimate.add_estimator(self) return estimate def build_first_stage_features(self, data_df: pd.DataFrame): treatment_vals = data_df[self._target_estimand.treatment_variable] if len(self._observed_common_causes_names) > 0: observed_common_causes_vals = data_df[self._observed_common_causes_names] observed_common_causes_vals = pd.get_dummies(observed_common_causes_vals, drop_first=True) if self._effect_modifier_names: effect_modifiers_vals = data_df[self._effect_modifier_names] effect_modifiers_vals = pd.get_dummies(effect_modifiers_vals, drop_first=True) if type(treatment_vals) is not np.ndarray: treatment_vals = treatment_vals.to_numpy() if treatment_vals.shape[0] != data_df.shape[0]: raise ValueError("Provided treatment values and dataframe should have the same length.") # Bulding the feature matrix n_samples = treatment_vals.shape[0] self.logger.debug("Number of samples" + str(n_samples) + str(len(self._target_estimand.treatment_variable))) treatment_2d = treatment_vals.reshape((n_samples, len(self._target_estimand.treatment_variable))) if len(self._observed_common_causes_names) > 0: features = np.concatenate((treatment_2d, observed_common_causes_vals), axis=1) else: features = treatment_2d if self._effect_modifier_names: for i in range(treatment_2d.shape[1]): curr_treatment = treatment_2d[:, i] new_features = curr_treatment[:, np.newaxis] * effect_modifiers_vals.to_numpy() features = np.concatenate((features, new_features), axis=1) features = features.astype( float, copy=False ) # converting to float in case of binary treatment and no other variables # features = sm.add_constant(features, has_constant='add') # to add an intercept term return features def construct_symbolic_estimator( self, first_stage_symbolic, second_stage_symbolic, total_effect_symbolic=None, estimand_type=None ): nie_symbolic = "(" + first_stage_symbolic + ")*(" + second_stage_symbolic + ")" if estimand_type == EstimandType.NONPARAMETRIC_NIE: return nie_symbolic elif estimand_type == EstimandType.NONPARAMETRIC_NDE: return "(" + total_effect_symbolic + ") - (" + nie_symbolic + ")"

andresmor-ms

325cf4e245de3e55b85a42c5fefc36f6ef34db46

c3e1c75696a8297aa48977ea4c7b7e8dc50dc6aa

treatment name parameter can be avoided here too

amit-sharma

py-why/dowhy

Add Python 3.10 support

* Add Python version condition on `autogluon-tabular`. * Remove `autogluon-tabular` from dev-dependencies to add Python 3.10 to our builds. **Note**: `autogluon-tabular` has a dependency constraint on `scikit-learn` of `<1.2.0`. So we're able to advance `scikit-learn` past `1.0.2`, but not to the most recent version. **Note**: `econml` has a transitive dependency on `numba`, which requires Python `<3.11`, and our `tensorflow` dev-dep has a range of `<3.11`.

2022-12-13 17:13:03+00:00

2022-12-15 14:13:24+00:00

pyproject.toml

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = ["PyWhy Community <amshar@microsoft.com>"] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/py-why/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model', ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [build-system] requires = ["poetry-core>=1.0.0"] build-backend = "poetry.core.masonry.api" [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.8 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # [tool.poetry.dependencies] python = ">=3.8,<3.10" cython = "^0.29.32" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = { version = "^1.4.2", optional = true } joblib = "^1.1.0" pygraphviz = { version = "^1.9", optional = true } econml = { version = "*" } tqdm = "^4.64.0" causal-learn = "^0.1.3.0" autogluon-tabular = {extras = ["all"], version = "^0.6.0", optional = true} #Plotting Extra matplotlib = { version = "^3.5.3", optional = true } sphinx_design = "^0.3.0" [tool.poetry.extras] pygraphviz = ["pygraphviz"] pydot = ["pydot"] plotting = ["matplotlib"] autogluon = ["autogluon-tabular"] [tool.poetry.group.dev.dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = { version = "^22.6.0", extras = ["jupyter"] } isort = "^5.10.1" pytest = "^7.1.2" pytest-cov = "^3.0.0" pytest-split = "^0.8.0" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.7.0" mypy = "^0.971" autogluon-tabular = {extras = ["all"], version = "^0.6.0"} [tool.poetry.group.docs] optional = true [tool.poetry.group.docs.dependencies] # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx = "^5.3.0" sphinxcontrib-googleanalytics = { git = "https://github.com/sphinx-contrib/googleanalytics.git", branch = "master" } nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" ipykernel = "^6.15.1" sphinx-copybutton = "0.5.0" seaborn = "^0.12.1" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = { version = "7.0.0rc3", allow-prereleases = true } [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates.", "notebook: jupyter notebook tests", "focused: a debug marker to focus on specific tests" ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' _black_check = 'black --check .' _isort_check = 'isort --check .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_durations = "poetry run poe test --store-durations" test_advanced = "pytest -v" test_focused = "pytest -v -m 'focused'" [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.format_check] sequence = ['_black_check', '_isort_check'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'format_check', 'test'] ignore_fail = "return_non_zero" [tool.black] line-length = 120 target-version = ['py38'] include = '\.pyi?$' extend-exclude = ''' ( __pycache__ | \.github ) ''' [tool.pylint] max-line-length = 120 disable = ["W0511"] [tool.isort] profile = 'black' multi_line_output = 3 line_length = 120 py_version = 38

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = ["PyWhy Community <amshar@microsoft.com>"] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/py-why/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', 'Programming Language :: Python :: 3.10', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model', ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [build-system] requires = ["poetry-core>=1.0.0"] build-backend = "poetry.core.masonry.api" [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * autogluon requires scikit-learn <1.2.0 # * numba (imported by econml) requires python <3.11 # [tool.poetry.dependencies] python = ">=3.8,<3.11" cython = "^0.29.32" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "<1.2.0" pydot = { version = "^1.4.2", optional = true } joblib = "^1.1.0" pygraphviz = { version = "^1.9", optional = true } econml = { version = "*" } tqdm = "^4.64.0" causal-learn = "^0.1.3.0" autogluon-tabular = { extras = [ "all", ], version = "^0.6.0", optional = true, python = "<3.10" } #Plotting Extra matplotlib = { version = "^3.5.3", optional = true } sphinx_design = "^0.3.0" [tool.poetry.extras] pygraphviz = ["pygraphviz"] pydot = ["pydot"] plotting = ["matplotlib"] autogluon = ["autogluon-tabular"] [tool.poetry.group.dev.dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = { version = "^22.6.0", extras = ["jupyter"] } isort = "^5.10.1" pytest = "^7.1.2" pytest-cov = "^3.0.0" pytest-split = "^0.8.0" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" keras = "^2.9.0" xgboost = "^1.7.0" mypy = "^0.971" [tool.poetry.group.docs] optional = true [tool.poetry.group.docs.dependencies] # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx = "^5.3.0" sphinxcontrib-googleanalytics = { git = "https://github.com/sphinx-contrib/googleanalytics.git", branch = "master" } nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" ipykernel = "^6.15.1" sphinx-copybutton = "0.5.0" seaborn = "^0.12.1" tensorflow = "^2.11.0" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = { version = "7.0.0rc3", allow-prereleases = true } [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates.", "notebook: jupyter notebook tests", "focused: a debug marker to focus on specific tests", ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' _black_check = 'black --check .' _isort_check = 'isort --check .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_durations = "poetry run poe test --store-durations" test_advanced = "pytest -v" test_focused = "pytest -v -m 'focused'" [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.format_check] sequence = ['_black_check', '_isort_check'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'format_check', 'test'] ignore_fail = "return_non_zero" [tool.black] line-length = 120 target-version = ['py38'] include = '\.pyi?$' extend-exclude = ''' ( __pycache__ | \.github ) ''' [tool.pylint] max-line-length = 120 disable = ["W0511"] [tool.isort] profile = 'black' multi_line_output = 3 line_length = 120 py_version = 38

darthtrevino

5bbac57b8104d99b03bd5e439a7c671bc7215303

7c6f56fb9023b023e694beba51656d826d9c1843

Is tensorflow still required? I thought this was only a dependency of autogluon.

petergtz

py-why/dowhy

Add Python 3.10 support

* Add Python version condition on `autogluon-tabular`. * Remove `autogluon-tabular` from dev-dependencies to add Python 3.10 to our builds. **Note**: `autogluon-tabular` has a dependency constraint on `scikit-learn` of `<1.2.0`. So we're able to advance `scikit-learn` past `1.0.2`, but not to the most recent version. **Note**: `econml` has a transitive dependency on `numba`, which requires Python `<3.11`, and our `tensorflow` dev-dep has a range of `<3.11`.

2022-12-13 17:13:03+00:00

2022-12-15 14:13:24+00:00

tests/gcm/ml/test_autogluon.py

import tempfile import numpy as np from flaky import flaky from pytest import approx from sklearn.model_selection import train_test_split from dowhy.gcm.fcms import AdditiveNoiseModel, ClassifierFCM from dowhy.gcm.ml.autolguon import AutoGluonClassifier, AutoGluonRegressor from dowhy.gcm.util.general import shape_into_2d @flaky(max_runs=3) def test_given_linear_categorical_data_when_using_auto_gluon_classifier_linear_then_provides_good_fit(): X, y = _generate_linear_classification_data(num_samples=1000, noise_std=0.2) x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.5) y_test = shape_into_2d(y_test) with tempfile.TemporaryDirectory() as temp_dir: model = AutoGluonClassifier(path=temp_dir, time_limit=60, hyperparameters={"LR": {}}) model.fit(x_train, y_train) assert np.sum(model.predict(x_test).squeeze() == y_test.squeeze()) / x_test.shape[0] == approx(1, abs=0.1) @flaky(max_runs=3) def test_given_linear_continuous_data_when_using_auto_gluon_regressor_linear_then_provides_good_fit(): X, y, _ = _generate_linear_data(num_samples=2000, noise_std=0.2) x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.5) y_test = shape_into_2d(y_test) with tempfile.TemporaryDirectory() as temp_dir: model = AutoGluonRegressor(path=temp_dir, time_limit=60, hyperparameters={"LR": {}}) model.fit(x_train, y_train) assert np.std(model.predict(x_test) - y_test) == approx(0.2, abs=1) def test_given_classifier_fcm_with_autogluon_classifier_model_when_drawing_samples_then_returns_samples(): with tempfile.TemporaryDirectory() as temp_dir: autogluon_sem = ClassifierFCM(AutoGluonClassifier(path=temp_dir, time_limit=5)) autogluon_sem.fit(np.random.normal(0, 1, (100, 3)), np.random.choice(3, 100, replace=True).astype(str)) autogluon_sem.draw_samples(np.random.normal(0, 1, (5, 3))) def test_given_anm_with_autogluon_regressor_model_when_drawing_samples_then_returns_samples(): with tempfile.TemporaryDirectory() as temp_dir: autogluon_sem = AdditiveNoiseModel(AutoGluonClassifier(path=temp_dir, time_limit=5)) autogluon_sem.fit(np.random.normal(0, 1, (100, 3)), np.random.normal(0, 1, (100, 1))) autogluon_sem.draw_samples(np.random.normal(0, 1, (5, 3))) def _generate_linear_data(num_samples: int, noise_std: float): num_features = int(np.random.choice(20, 1) + 1) coefficients = np.random.uniform(-5, 5, num_features) X = np.random.normal(0, 1, (num_samples, num_features)) y = np.sum(coefficients * X, axis=1) + np.random.normal(0, noise_std, num_samples) return X, y, coefficients def _generate_linear_classification_data(num_samples: int, noise_std: float): X, y, _ = _generate_linear_data(num_samples, noise_std) y = y > np.median(y) return X, y.astype(str)

import tempfile import numpy as np from flaky import flaky from pytest import approx, importorskip, mark from sklearn.model_selection import train_test_split from dowhy.gcm.fcms import AdditiveNoiseModel, ClassifierFCM autolguon = importorskip("dowhy.gcm.ml.autolguon") from dowhy.gcm.ml.autolguon import AutoGluonClassifier, AutoGluonRegressor from dowhy.gcm.util.general import shape_into_2d @flaky(max_runs=3) def test_given_linear_categorical_data_when_using_auto_gluon_classifier_linear_then_provides_good_fit(): X, y = _generate_linear_classification_data(num_samples=1000, noise_std=0.2) x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.5) y_test = shape_into_2d(y_test) with tempfile.TemporaryDirectory() as temp_dir: model = AutoGluonClassifier(path=temp_dir, time_limit=60, hyperparameters={"LR": {}}) model.fit(x_train, y_train) assert np.sum(model.predict(x_test).squeeze() == y_test.squeeze()) / x_test.shape[0] == approx(1, abs=0.1) @flaky(max_runs=3) def test_given_linear_continuous_data_when_using_auto_gluon_regressor_linear_then_provides_good_fit(): X, y, _ = _generate_linear_data(num_samples=2000, noise_std=0.2) x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.5) y_test = shape_into_2d(y_test) with tempfile.TemporaryDirectory() as temp_dir: model = AutoGluonRegressor(path=temp_dir, time_limit=60, hyperparameters={"LR": {}}) model.fit(x_train, y_train) assert np.std(model.predict(x_test) - y_test) == approx(0.2, abs=1) def test_given_classifier_fcm_with_autogluon_classifier_model_when_drawing_samples_then_returns_samples(): with tempfile.TemporaryDirectory() as temp_dir: autogluon_sem = ClassifierFCM(AutoGluonClassifier(path=temp_dir, time_limit=5)) autogluon_sem.fit(np.random.normal(0, 1, (100, 3)), np.random.choice(3, 100, replace=True).astype(str)) autogluon_sem.draw_samples(np.random.normal(0, 1, (5, 3))) def test_given_anm_with_autogluon_regressor_model_when_drawing_samples_then_returns_samples(): with tempfile.TemporaryDirectory() as temp_dir: autogluon_sem = AdditiveNoiseModel(AutoGluonClassifier(path=temp_dir, time_limit=5)) autogluon_sem.fit(np.random.normal(0, 1, (100, 3)), np.random.normal(0, 1, (100, 1))) autogluon_sem.draw_samples(np.random.normal(0, 1, (5, 3))) def _generate_linear_data(num_samples: int, noise_std: float): num_features = int(np.random.choice(20, 1) + 1) coefficients = np.random.uniform(-5, 5, num_features) X = np.random.normal(0, 1, (num_samples, num_features)) y = np.sum(coefficients * X, axis=1) + np.random.normal(0, noise_std, num_samples) return X, y, coefficients def _generate_linear_classification_data(num_samples: int, noise_std: float): X, y, _ = _generate_linear_data(num_samples, noise_std) y = y > np.median(y) return X, y.astype(str)

darthtrevino

5bbac57b8104d99b03bd5e439a7c671bc7215303

7c6f56fb9023b023e694beba51656d826d9c1843

I think for this there's a better way to do it. Reading https://docs.pytest.org/en/7.1.x/how-to/skipping.html#skipping-on-a-missing-import-dependency it should be possible to do: ```python autolguon = pytest.importorskip("dowhy.gcm.ml.autolguon") from dowhy.gcm.ml.autolguon import AutoGluonClassifier, AutoGluonRegressor ``` This would avoid commenting out code. I just pushed a new commit trying this out.

petergtz

py-why/dowhy

Add Python 3.10 support

* Add Python version condition on `autogluon-tabular`. * Remove `autogluon-tabular` from dev-dependencies to add Python 3.10 to our builds. **Note**: `autogluon-tabular` has a dependency constraint on `scikit-learn` of `<1.2.0`. So we're able to advance `scikit-learn` past `1.0.2`, but not to the most recent version. **Note**: `econml` has a transitive dependency on `numba`, which requires Python `<3.11`, and our `tensorflow` dev-dep has a range of `<3.11`.

2022-12-13 17:13:03+00:00

2022-12-15 14:13:24+00:00

tests/gcm/test_auto.py

import networkx as nx import numpy as np import pandas as pd from flaky import flaky from sklearn.ensemble import HistGradientBoostingClassifier, HistGradientBoostingRegressor from sklearn.linear_model import ElasticNetCV, LassoCV, LinearRegression, LogisticRegression, RidgeCV from sklearn.naive_bayes import GaussianNB from sklearn.pipeline import Pipeline from dowhy.gcm import ProbabilisticCausalModel from dowhy.gcm.auto import AssignmentQuality, assign_causal_mechanisms from dowhy.gcm.ml import AutoGluonClassifier, AutoGluonRegressor def _generate_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) return X, Y def _generate_non_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(np.log(abs(X)), axis=1) return X, Y def _generate_linear_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) > 0).astype(str) return X, Y def _generate_non_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(np.exp(X), axis=1) > np.median(np.sum(np.exp(X), axis=1))).astype(str) return X, Y @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").prediction_model.sklearn_model, HistGradientBoostingRegressor ) or isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LassoCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, ElasticNetCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, RidgeCV) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").classifier_model.sklearn_model, HistGradientBoostingClassifier ) or isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, GaussianNB) @flaky(max_runs=3) def test_given_polynomial_regression_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.column_stack( [np.random.choice(2, 100, replace=True).astype(str), np.random.normal(0, 1, (100, 2)).astype(object)] ).astype(object) Y = [] for i in range(X.shape[0]): Y.append(X[i, 1] * X[i, 2] if X[i, 0] == "0" else X[i, 1] + X[i, 2]) Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER, override_models=True) @flaky(max_runs=3) def test_given_polynomial_classification_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.random.normal(0, 1, (100, 2)) Y = [] for x in X: if x[0] * x[1] > 0: Y.append("Class 0") else: Y.append("Class 1") Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD, override_models=True) def test_when_auto_called_from_main_namespace_returns_no_attribute_error(): from dowhy import gcm _ = gcm.auto.AssignmentQuality.GOOD def test_when_using_best_quality_then_returns_auto_gluon_model(): causal_model = ProbabilisticCausalModel(nx.DiGraph([("X", "Y")])) assign_causal_mechanisms(causal_model, pd.DataFrame({"X": [1], "Y": [1]}), quality=AssignmentQuality.BEST) assert isinstance(causal_model.causal_mechanism("Y").prediction_model, AutoGluonRegressor) assign_causal_mechanisms( causal_model, pd.DataFrame({"X": [1], "Y": ["Class 1"]}), quality=AssignmentQuality.BEST, override_models=True ) assert isinstance(causal_model.causal_mechanism("Y").classifier_model, AutoGluonClassifier)

import networkx as nx import numpy as np import pandas as pd from flaky import flaky from pytest import mark from sklearn.ensemble import HistGradientBoostingClassifier, HistGradientBoostingRegressor from sklearn.linear_model import ElasticNetCV, LassoCV, LinearRegression, LogisticRegression, RidgeCV from sklearn.naive_bayes import GaussianNB from sklearn.pipeline import Pipeline from dowhy.gcm import ProbabilisticCausalModel from dowhy.gcm.auto import AssignmentQuality, assign_causal_mechanisms def _generate_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) return X, Y def _generate_non_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(np.log(abs(X)), axis=1) return X, Y def _generate_linear_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) > 0).astype(str) return X, Y def _generate_non_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(np.exp(X), axis=1) > np.median(np.sum(np.exp(X), axis=1))).astype(str) return X, Y @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").prediction_model.sklearn_model, HistGradientBoostingRegressor ) or isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LassoCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, ElasticNetCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, RidgeCV) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").classifier_model.sklearn_model, HistGradientBoostingClassifier ) or isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, GaussianNB) @flaky(max_runs=3) def test_given_polynomial_regression_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.column_stack( [np.random.choice(2, 100, replace=True).astype(str), np.random.normal(0, 1, (100, 2)).astype(object)] ).astype(object) Y = [] for i in range(X.shape[0]): Y.append(X[i, 1] * X[i, 2] if X[i, 0] == "0" else X[i, 1] + X[i, 2]) Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER, override_models=True) @flaky(max_runs=3) def test_given_polynomial_classification_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.random.normal(0, 1, (100, 2)) Y = [] for x in X: if x[0] * x[1] > 0: Y.append("Class 0") else: Y.append("Class 1") Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD, override_models=True) def test_when_auto_called_from_main_namespace_returns_no_attribute_error(): from dowhy import gcm _ = gcm.auto.AssignmentQuality.GOOD @mark.skip("Not running AutoGluon-based tests as part of CI yet.") def test_when_using_best_quality_then_returns_auto_gluon_model(): from dowhy.gcm.ml import AutoGluonClassifier, AutoGluonRegressor causal_model = ProbabilisticCausalModel(nx.DiGraph([("X", "Y")])) assign_causal_mechanisms(causal_model, pd.DataFrame({"X": [1], "Y": [1]}), quality=AssignmentQuality.BEST) assert isinstance(causal_model.causal_mechanism("Y").prediction_model, AutoGluonRegressor) assign_causal_mechanisms( causal_model, pd.DataFrame({"X": [1], "Y": ["Class 1"]}), quality=AssignmentQuality.BEST, override_models=True ) assert isinstance(causal_model.causal_mechanism("Y").classifier_model, AutoGluonClassifier)

darthtrevino

5bbac57b8104d99b03bd5e439a7c671bc7215303

7c6f56fb9023b023e694beba51656d826d9c1843

With the skip marker, is it really necessary to comment out the code? Is PyTest not entirely skipping this test? Assuming that, we can simply move the `AutoGluonClassifier` import into the test function itself. I just pushed a new commit trying this out.

petergtz

py-why/dowhy

Add Python 3.10 support

* Add Python version condition on `autogluon-tabular`. * Remove `autogluon-tabular` from dev-dependencies to add Python 3.10 to our builds. **Note**: `autogluon-tabular` has a dependency constraint on `scikit-learn` of `<1.2.0`. So we're able to advance `scikit-learn` past `1.0.2`, but not to the most recent version. **Note**: `econml` has a transitive dependency on `numba`, which requires Python `<3.11`, and our `tensorflow` dev-dep has a range of `<3.11`.

2022-12-13 17:13:03+00:00

2022-12-15 14:13:24+00:00

tests/gcm/test_auto.py

import networkx as nx import numpy as np import pandas as pd from flaky import flaky from sklearn.ensemble import HistGradientBoostingClassifier, HistGradientBoostingRegressor from sklearn.linear_model import ElasticNetCV, LassoCV, LinearRegression, LogisticRegression, RidgeCV from sklearn.naive_bayes import GaussianNB from sklearn.pipeline import Pipeline from dowhy.gcm import ProbabilisticCausalModel from dowhy.gcm.auto import AssignmentQuality, assign_causal_mechanisms from dowhy.gcm.ml import AutoGluonClassifier, AutoGluonRegressor def _generate_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) return X, Y def _generate_non_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(np.log(abs(X)), axis=1) return X, Y def _generate_linear_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) > 0).astype(str) return X, Y def _generate_non_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(np.exp(X), axis=1) > np.median(np.sum(np.exp(X), axis=1))).astype(str) return X, Y @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").prediction_model.sklearn_model, HistGradientBoostingRegressor ) or isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LassoCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, ElasticNetCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, RidgeCV) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").classifier_model.sklearn_model, HistGradientBoostingClassifier ) or isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, GaussianNB) @flaky(max_runs=3) def test_given_polynomial_regression_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.column_stack( [np.random.choice(2, 100, replace=True).astype(str), np.random.normal(0, 1, (100, 2)).astype(object)] ).astype(object) Y = [] for i in range(X.shape[0]): Y.append(X[i, 1] * X[i, 2] if X[i, 0] == "0" else X[i, 1] + X[i, 2]) Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER, override_models=True) @flaky(max_runs=3) def test_given_polynomial_classification_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.random.normal(0, 1, (100, 2)) Y = [] for x in X: if x[0] * x[1] > 0: Y.append("Class 0") else: Y.append("Class 1") Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD, override_models=True) def test_when_auto_called_from_main_namespace_returns_no_attribute_error(): from dowhy import gcm _ = gcm.auto.AssignmentQuality.GOOD def test_when_using_best_quality_then_returns_auto_gluon_model(): causal_model = ProbabilisticCausalModel(nx.DiGraph([("X", "Y")])) assign_causal_mechanisms(causal_model, pd.DataFrame({"X": [1], "Y": [1]}), quality=AssignmentQuality.BEST) assert isinstance(causal_model.causal_mechanism("Y").prediction_model, AutoGluonRegressor) assign_causal_mechanisms( causal_model, pd.DataFrame({"X": [1], "Y": ["Class 1"]}), quality=AssignmentQuality.BEST, override_models=True ) assert isinstance(causal_model.causal_mechanism("Y").classifier_model, AutoGluonClassifier)

import networkx as nx import numpy as np import pandas as pd from flaky import flaky from pytest import mark from sklearn.ensemble import HistGradientBoostingClassifier, HistGradientBoostingRegressor from sklearn.linear_model import ElasticNetCV, LassoCV, LinearRegression, LogisticRegression, RidgeCV from sklearn.naive_bayes import GaussianNB from sklearn.pipeline import Pipeline from dowhy.gcm import ProbabilisticCausalModel from dowhy.gcm.auto import AssignmentQuality, assign_causal_mechanisms def _generate_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) return X, Y def _generate_non_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(np.log(abs(X)), axis=1) return X, Y def _generate_linear_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) > 0).astype(str) return X, Y def _generate_non_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(np.exp(X), axis=1) > np.median(np.sum(np.exp(X), axis=1))).astype(str) return X, Y @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").prediction_model.sklearn_model, HistGradientBoostingRegressor ) or isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LassoCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, ElasticNetCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, RidgeCV) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").classifier_model.sklearn_model, HistGradientBoostingClassifier ) or isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, GaussianNB) @flaky(max_runs=3) def test_given_polynomial_regression_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.column_stack( [np.random.choice(2, 100, replace=True).astype(str), np.random.normal(0, 1, (100, 2)).astype(object)] ).astype(object) Y = [] for i in range(X.shape[0]): Y.append(X[i, 1] * X[i, 2] if X[i, 0] == "0" else X[i, 1] + X[i, 2]) Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER, override_models=True) @flaky(max_runs=3) def test_given_polynomial_classification_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.random.normal(0, 1, (100, 2)) Y = [] for x in X: if x[0] * x[1] > 0: Y.append("Class 0") else: Y.append("Class 1") Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD, override_models=True) def test_when_auto_called_from_main_namespace_returns_no_attribute_error(): from dowhy import gcm _ = gcm.auto.AssignmentQuality.GOOD @mark.skip("Not running AutoGluon-based tests as part of CI yet.") def test_when_using_best_quality_then_returns_auto_gluon_model(): from dowhy.gcm.ml import AutoGluonClassifier, AutoGluonRegressor causal_model = ProbabilisticCausalModel(nx.DiGraph([("X", "Y")])) assign_causal_mechanisms(causal_model, pd.DataFrame({"X": [1], "Y": [1]}), quality=AssignmentQuality.BEST) assert isinstance(causal_model.causal_mechanism("Y").prediction_model, AutoGluonRegressor) assign_causal_mechanisms( causal_model, pd.DataFrame({"X": [1], "Y": ["Class 1"]}), quality=AssignmentQuality.BEST, override_models=True ) assert isinstance(causal_model.causal_mechanism("Y").classifier_model, AutoGluonClassifier)

darthtrevino

5bbac57b8104d99b03bd5e439a7c671bc7215303

7c6f56fb9023b023e694beba51656d826d9c1843

I think the reasoning was that the import would fail, but let's see what it does

darthtrevino

py-why/dowhy

Add Python 3.10 support

* Add Python version condition on `autogluon-tabular`. * Remove `autogluon-tabular` from dev-dependencies to add Python 3.10 to our builds. **Note**: `autogluon-tabular` has a dependency constraint on `scikit-learn` of `<1.2.0`. So we're able to advance `scikit-learn` past `1.0.2`, but not to the most recent version. **Note**: `econml` has a transitive dependency on `numba`, which requires Python `<3.11`, and our `tensorflow` dev-dep has a range of `<3.11`.

2022-12-13 17:13:03+00:00

2022-12-15 14:13:24+00:00

tests/gcm/test_auto.py

import networkx as nx import numpy as np import pandas as pd from flaky import flaky from sklearn.ensemble import HistGradientBoostingClassifier, HistGradientBoostingRegressor from sklearn.linear_model import ElasticNetCV, LassoCV, LinearRegression, LogisticRegression, RidgeCV from sklearn.naive_bayes import GaussianNB from sklearn.pipeline import Pipeline from dowhy.gcm import ProbabilisticCausalModel from dowhy.gcm.auto import AssignmentQuality, assign_causal_mechanisms from dowhy.gcm.ml import AutoGluonClassifier, AutoGluonRegressor def _generate_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) return X, Y def _generate_non_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(np.log(abs(X)), axis=1) return X, Y def _generate_linear_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) > 0).astype(str) return X, Y def _generate_non_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(np.exp(X), axis=1) > np.median(np.sum(np.exp(X), axis=1))).astype(str) return X, Y @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").prediction_model.sklearn_model, HistGradientBoostingRegressor ) or isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LassoCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, ElasticNetCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, RidgeCV) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").classifier_model.sklearn_model, HistGradientBoostingClassifier ) or isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, GaussianNB) @flaky(max_runs=3) def test_given_polynomial_regression_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.column_stack( [np.random.choice(2, 100, replace=True).astype(str), np.random.normal(0, 1, (100, 2)).astype(object)] ).astype(object) Y = [] for i in range(X.shape[0]): Y.append(X[i, 1] * X[i, 2] if X[i, 0] == "0" else X[i, 1] + X[i, 2]) Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER, override_models=True) @flaky(max_runs=3) def test_given_polynomial_classification_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.random.normal(0, 1, (100, 2)) Y = [] for x in X: if x[0] * x[1] > 0: Y.append("Class 0") else: Y.append("Class 1") Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD, override_models=True) def test_when_auto_called_from_main_namespace_returns_no_attribute_error(): from dowhy import gcm _ = gcm.auto.AssignmentQuality.GOOD def test_when_using_best_quality_then_returns_auto_gluon_model(): causal_model = ProbabilisticCausalModel(nx.DiGraph([("X", "Y")])) assign_causal_mechanisms(causal_model, pd.DataFrame({"X": [1], "Y": [1]}), quality=AssignmentQuality.BEST) assert isinstance(causal_model.causal_mechanism("Y").prediction_model, AutoGluonRegressor) assign_causal_mechanisms( causal_model, pd.DataFrame({"X": [1], "Y": ["Class 1"]}), quality=AssignmentQuality.BEST, override_models=True ) assert isinstance(causal_model.causal_mechanism("Y").classifier_model, AutoGluonClassifier)

import networkx as nx import numpy as np import pandas as pd from flaky import flaky from pytest import mark from sklearn.ensemble import HistGradientBoostingClassifier, HistGradientBoostingRegressor from sklearn.linear_model import ElasticNetCV, LassoCV, LinearRegression, LogisticRegression, RidgeCV from sklearn.naive_bayes import GaussianNB from sklearn.pipeline import Pipeline from dowhy.gcm import ProbabilisticCausalModel from dowhy.gcm.auto import AssignmentQuality, assign_causal_mechanisms def _generate_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) return X, Y def _generate_non_linear_regression_data(): X = np.random.normal(0, 1, (1000, 5)) Y = np.sum(np.log(abs(X)), axis=1) return X, Y def _generate_linear_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(X * np.random.uniform(-5, 5, X.shape[1]), axis=1) > 0).astype(str) return X, Y def _generate_non_classification_data(): X = np.random.normal(0, 1, (1000, 5)) Y = (np.sum(np.exp(X), axis=1) > np.median(np.sum(np.exp(X), axis=1))).astype(str) return X, Y @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").prediction_model.sklearn_model, HistGradientBoostingRegressor ) or isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_regression_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_linear_regression_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LinearRegression) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, LassoCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, ElasticNetCV) assert not isinstance(causal_model.causal_mechanism("Y").prediction_model.sklearn_model, RidgeCV) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_linear_model(): X, Y = _generate_linear_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_good_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assert isinstance( causal_model.causal_mechanism("Y").classifier_model.sklearn_model, HistGradientBoostingClassifier ) or isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, Pipeline) @flaky(max_runs=3) def test_given_non_linear_classification_problem_when_auto_assign_causal_models_with_better_quality_returns_non_linear_model(): X, Y = _generate_non_classification_data() causal_model = ProbabilisticCausalModel( nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y"), ("X3", "Y"), ("X4", "Y")]) ) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, LogisticRegression) assert not isinstance(causal_model.causal_mechanism("Y").classifier_model.sklearn_model, GaussianNB) @flaky(max_runs=3) def test_given_polynomial_regression_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.column_stack( [np.random.choice(2, 100, replace=True).astype(str), np.random.normal(0, 1, (100, 2)).astype(object)] ).astype(object) Y = [] for i in range(X.shape[0]): Y.append(X[i, 1] * X[i, 2] if X[i, 0] == "0" else X[i, 1] + X[i, 2]) Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y"), ("X2", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER, override_models=True) @flaky(max_runs=3) def test_given_polynomial_classification_data_with_categorical_input_when_auto_assign_causal_models_then_does_not_raise_error(): X = np.random.normal(0, 1, (100, 2)) Y = [] for x in X: if x[0] * x[1] > 0: Y.append("Class 0") else: Y.append("Class 1") Y = np.array(Y) causal_model = ProbabilisticCausalModel(nx.DiGraph([("X0", "Y"), ("X1", "Y")])) data = {"X" + str(i): X[:, i] for i in range(X.shape[1])} data.update({"Y": Y}) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.BETTER) assign_causal_mechanisms(causal_model, pd.DataFrame(data), quality=AssignmentQuality.GOOD, override_models=True) def test_when_auto_called_from_main_namespace_returns_no_attribute_error(): from dowhy import gcm _ = gcm.auto.AssignmentQuality.GOOD @mark.skip("Not running AutoGluon-based tests as part of CI yet.") def test_when_using_best_quality_then_returns_auto_gluon_model(): from dowhy.gcm.ml import AutoGluonClassifier, AutoGluonRegressor causal_model = ProbabilisticCausalModel(nx.DiGraph([("X", "Y")])) assign_causal_mechanisms(causal_model, pd.DataFrame({"X": [1], "Y": [1]}), quality=AssignmentQuality.BEST) assert isinstance(causal_model.causal_mechanism("Y").prediction_model, AutoGluonRegressor) assign_causal_mechanisms( causal_model, pd.DataFrame({"X": [1], "Y": ["Class 1"]}), quality=AssignmentQuality.BEST, override_models=True ) assert isinstance(causal_model.causal_mechanism("Y").classifier_model, AutoGluonClassifier)

darthtrevino

5bbac57b8104d99b03bd5e439a7c671bc7215303

7c6f56fb9023b023e694beba51656d826d9c1843

LGTM!

darthtrevino

py-why/dowhy

Make autogluon optional

It looks like since this has not been listed in the 'extra' group, it's not marked as optional. Right now, a `pip install dowhy` pulls in autogluon and pytorch and makes this a pretty large installation. I believe this change should fix this. Signed-off-by: Peter Goetz <pego@amazon.com>

2022-12-09 22:26:14+00:00

2022-12-12 09:07:24+00:00

pyproject.toml

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = ["PyWhy Community <amshar@microsoft.com>"] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/py-why/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model', ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [build-system] requires = ["poetry-core>=1.0.0"] build-backend = "poetry.core.masonry.api" [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.8 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.10 # [tool.poetry.dependencies] python = ">=3.8,<3.10" cython = "^0.29.32" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = { version = "^1.4.2", optional = true } joblib = "^1.1.0" pygraphviz = { version = "^1.9", optional = true } econml = { version = "*", optional = true } tqdm = "^4.64.0" causal-learn = "^0.1.3.0" autogluon-tabular = {extras = ["all"], version = "^0.6.0", optional = true} # CausalML Extra (causalml is wired to use llvmlite 0.36) causalml = { git = "https://github.com/uber/causalml", branch = "master", optional = true } llvmlite = { version = "^0.36.0", optional = true } #Plotting Extra matplotlib = { version = "^3.5.3", optional = true } sphinx_design = "^0.3.0" [tool.poetry.extras] econml = ["econml"] pygraphviz = ["pygraphviz"] pydot = ["pydot"] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite", "cython"] [tool.poetry.group.dev.dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = { version = "^22.6.0", extras = ["jupyter"] } isort = "^5.10.1" pytest = "^7.1.2" pytest-cov = "^3.0.0" pytest-split = "^0.8.0" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.7.0" mypy = "^0.971" autogluon-tabular = {extras = ["all"], version = "^0.6.0"} [tool.poetry.group.docs] optional = true [tool.poetry.group.docs.dependencies] # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx = "^5.3.0" sphinxcontrib-googleanalytics = { git = "https://github.com/sphinx-contrib/googleanalytics.git", branch = "master" } nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" ipykernel = "^6.15.1" sphinx-copybutton = "0.5.0" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = { version = "7.0.0rc3", allow-prereleases = true } [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates.", "notebook: jupyter notebook tests", "focused: a debug marker to focus on specific tests" ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' _black_check = 'black --check .' _isort_check = 'isort --check .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_durations = "poetry run poe test --store-durations" test_advanced = "pytest -v" test_focused = "pytest -v -m 'focused'" [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.format_check] sequence = ['_black_check', '_isort_check'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'format_check', 'test'] ignore_fail = "return_non_zero" [tool.black] line-length = 120 target-version = ['py38'] include = '\.pyi?$' extend-exclude = ''' ( __pycache__ | \.github ) ''' [tool.pylint] max-line-length = 120 disable = ["W0511"] [tool.isort] profile = 'black' multi_line_output = 3 line_length = 120 py_version = 38

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = ["PyWhy Community <amshar@microsoft.com>"] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/py-why/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model', ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [build-system] requires = ["poetry-core>=1.0.0"] build-backend = "poetry.core.masonry.api" [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.8 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.10 # [tool.poetry.dependencies] python = ">=3.8,<3.10" cython = "^0.29.32" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = { version = "^1.4.2", optional = true } joblib = "^1.1.0" pygraphviz = { version = "^1.9", optional = true } econml = { version = "*", optional = true } tqdm = "^4.64.0" causal-learn = "^0.1.3.0" autogluon-tabular = {extras = ["all"], version = "^0.6.0", optional = true} # CausalML Extra (causalml is wired to use llvmlite 0.36) causalml = { git = "https://github.com/uber/causalml", branch = "master", optional = true } llvmlite = { version = "^0.36.0", optional = true } #Plotting Extra matplotlib = { version = "^3.5.3", optional = true } sphinx_design = "^0.3.0" [tool.poetry.extras] econml = ["econml"] pygraphviz = ["pygraphviz"] pydot = ["pydot"] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite", "cython"] autogluon = ["autogluon-tabular"] [tool.poetry.group.dev.dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = { version = "^22.6.0", extras = ["jupyter"] } isort = "^5.10.1" pytest = "^7.1.2" pytest-cov = "^3.0.0" pytest-split = "^0.8.0" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.7.0" mypy = "^0.971" autogluon-tabular = {extras = ["all"], version = "^0.6.0"} [tool.poetry.group.docs] optional = true [tool.poetry.group.docs.dependencies] # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx = "^5.3.0" sphinxcontrib-googleanalytics = { git = "https://github.com/sphinx-contrib/googleanalytics.git", branch = "master" } nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" ipykernel = "^6.15.1" sphinx-copybutton = "0.5.0" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = { version = "7.0.0rc3", allow-prereleases = true } [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates.", "notebook: jupyter notebook tests", "focused: a debug marker to focus on specific tests" ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' _black_check = 'black --check .' _isort_check = 'isort --check .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_durations = "poetry run poe test --store-durations" test_advanced = "pytest -v" test_focused = "pytest -v -m 'focused'" [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.format_check] sequence = ['_black_check', '_isort_check'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'format_check', 'test'] ignore_fail = "return_non_zero" [tool.black] line-length = 120 target-version = ['py38'] include = '\.pyi?$' extend-exclude = ''' ( __pycache__ | \.github ) ''' [tool.pylint] max-line-length = 120 disable = ["W0511"] [tool.isort] profile = 'black' multi_line_output = 3 line_length = 120 py_version = 38

petergtz

6ebfc4464bd5c41880f25299df25c3c1cd05b20c

b5ae49a256217f1cae5a45033e8e6bc84599e508

I think the package name is autogluon.tabular.

bloebp

py-why/dowhy

Make autogluon optional

It looks like since this has not been listed in the 'extra' group, it's not marked as optional. Right now, a `pip install dowhy` pulls in autogluon and pytorch and makes this a pretty large installation. I believe this change should fix this. Signed-off-by: Peter Goetz <pego@amazon.com>

2022-12-09 22:26:14+00:00

2022-12-12 09:07:24+00:00

pyproject.toml

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = ["PyWhy Community <amshar@microsoft.com>"] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/py-why/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model', ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [build-system] requires = ["poetry-core>=1.0.0"] build-backend = "poetry.core.masonry.api" [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.8 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.10 # [tool.poetry.dependencies] python = ">=3.8,<3.10" cython = "^0.29.32" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = { version = "^1.4.2", optional = true } joblib = "^1.1.0" pygraphviz = { version = "^1.9", optional = true } econml = { version = "*", optional = true } tqdm = "^4.64.0" causal-learn = "^0.1.3.0" autogluon-tabular = {extras = ["all"], version = "^0.6.0", optional = true} # CausalML Extra (causalml is wired to use llvmlite 0.36) causalml = { git = "https://github.com/uber/causalml", branch = "master", optional = true } llvmlite = { version = "^0.36.0", optional = true } #Plotting Extra matplotlib = { version = "^3.5.3", optional = true } sphinx_design = "^0.3.0" [tool.poetry.extras] econml = ["econml"] pygraphviz = ["pygraphviz"] pydot = ["pydot"] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite", "cython"] [tool.poetry.group.dev.dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = { version = "^22.6.0", extras = ["jupyter"] } isort = "^5.10.1" pytest = "^7.1.2" pytest-cov = "^3.0.0" pytest-split = "^0.8.0" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.7.0" mypy = "^0.971" autogluon-tabular = {extras = ["all"], version = "^0.6.0"} [tool.poetry.group.docs] optional = true [tool.poetry.group.docs.dependencies] # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx = "^5.3.0" sphinxcontrib-googleanalytics = { git = "https://github.com/sphinx-contrib/googleanalytics.git", branch = "master" } nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" ipykernel = "^6.15.1" sphinx-copybutton = "0.5.0" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = { version = "7.0.0rc3", allow-prereleases = true } [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates.", "notebook: jupyter notebook tests", "focused: a debug marker to focus on specific tests" ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' _black_check = 'black --check .' _isort_check = 'isort --check .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_durations = "poetry run poe test --store-durations" test_advanced = "pytest -v" test_focused = "pytest -v -m 'focused'" [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.format_check] sequence = ['_black_check', '_isort_check'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'format_check', 'test'] ignore_fail = "return_non_zero" [tool.black] line-length = 120 target-version = ['py38'] include = '\.pyi?$' extend-exclude = ''' ( __pycache__ | \.github ) ''' [tool.pylint] max-line-length = 120 disable = ["W0511"] [tool.isort] profile = 'black' multi_line_output = 3 line_length = 120 py_version = 38

[tool.poetry] name = "dowhy" # # 0.0.0 is standard placeholder for poetry-dynamic-versioning # any changes to this should not be checked in # version = "0.0.0" description = "DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions" authors = ["PyWhy Community <amshar@microsoft.com>"] maintainers = [] license = "MIT" documentation = "https://py-why.github.io/dowhy" repository = "https://github.com/py-why/dowhy" classifiers = [ 'Development Status :: 4 - Beta', 'License :: OSI Approved :: MIT License', 'Programming Language :: Python :: 3.8', 'Programming Language :: Python :: 3.9', ] keywords = [ 'causality', 'machine-learning', 'causal-inference', 'statistics', 'graphical-model', ] include = ['docs', 'tests', 'CONTRIBUTING.md', 'LICENSE'] readme = 'README.rst' [build-system] requires = ["poetry-core>=1.0.0"] build-backend = "poetry.core.masonry.api" [tool.poetry-dynamic-versioning] enable = true vcs = "git" [tool.poetry-dynamic-versioning.substitution] files = ["dowhy/__init__.py"] # # Dependency compatibility notes: # * xgboost requires Python >=3.8 # * pygraphviz requires Python >=3.8 # * networkx requires Python >= 3.8 # * llvmlite requires Python >=3.6,<3.10 # [tool.poetry.dependencies] python = ">=3.8,<3.10" cython = "^0.29.32" scipy = "^1.8.1" statsmodels = "^0.13.2" numpy = "^1.23.1" pandas = "^1.4.3" networkx = "^2.8.5" sympy = "^1.10.1" scikit-learn = "1.0.2" pydot = { version = "^1.4.2", optional = true } joblib = "^1.1.0" pygraphviz = { version = "^1.9", optional = true } econml = { version = "*", optional = true } tqdm = "^4.64.0" causal-learn = "^0.1.3.0" autogluon-tabular = {extras = ["all"], version = "^0.6.0", optional = true} # CausalML Extra (causalml is wired to use llvmlite 0.36) causalml = { git = "https://github.com/uber/causalml", branch = "master", optional = true } llvmlite = { version = "^0.36.0", optional = true } #Plotting Extra matplotlib = { version = "^3.5.3", optional = true } sphinx_design = "^0.3.0" [tool.poetry.extras] econml = ["econml"] pygraphviz = ["pygraphviz"] pydot = ["pydot"] plotting = ["matplotlib"] causalml = ["causalml", "llvmlite", "cython"] autogluon = ["autogluon-tabular"] [tool.poetry.group.dev.dependencies] poethepoet = "^0.16.0" flake8 = "^4.0.1" black = { version = "^22.6.0", extras = ["jupyter"] } isort = "^5.10.1" pytest = "^7.1.2" pytest-cov = "^3.0.0" pytest-split = "^0.8.0" nbformat = "^5.4.0" jupyter = "^1.0.0" flaky = "^3.7.0" tensorflow = "^2.9.1" keras = "^2.9.0" xgboost = "^1.7.0" mypy = "^0.971" autogluon-tabular = {extras = ["all"], version = "^0.6.0"} [tool.poetry.group.docs] optional = true [tool.poetry.group.docs.dependencies] # # Dependencies for Documentation Generation # rpy2 = "^3.5.2" sphinx = "^5.3.0" sphinxcontrib-googleanalytics = { git = "https://github.com/sphinx-contrib/googleanalytics.git", branch = "master" } nbsphinx = "^0.8.9" sphinx-rtd-theme = "^1.0.0" pydata-sphinx-theme = "^0.9.0" ipykernel = "^6.15.1" sphinx-copybutton = "0.5.0" # # Versions defined for security reasons # # https://github.com/py-why/dowhy/security/dependabot/1 - CVE-2022-34749 nbconvert = { version = "7.0.0rc3", allow-prereleases = true } [tool.pytest.ini_options] markers = [ "advanced: not be to run each time. only on package updates.", "notebook: jupyter notebook tests", "focused: a debug marker to focus on specific tests" ] [tool.poe.tasks] # stop the build if there are Python syntax errors or undefined names _flake8Errors = "flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics" _flake8Warnings = "flake8 . --count --exit-zero --statistics" _black = 'black .' _isort = 'isort .' _black_check = 'black --check .' _isort_check = 'isort --check .' # testing tasks test = "pytest -v -m 'not advanced' --durations=0 --durations-min=60.0" test_durations = "poetry run poe test --store-durations" test_advanced = "pytest -v" test_focused = "pytest -v -m 'focused'" [tool.poe.tasks.format] sequence = ['_black', '_isort'] ignore_fail = 'return_non_zero' [tool.poe.tasks.format_check] sequence = ['_black_check', '_isort_check'] ignore_fail = 'return_non_zero' [tool.poe.tasks.lint] sequence = ['_flake8Errors', '_flake8Warnings'] ignore_fail = 'return_non_zero' [tool.poe.tasks.verify] sequence = ['lint', 'format_check', 'test'] ignore_fail = "return_non_zero" [tool.black] line-length = 120 target-version = ['py38'] include = '\.pyi?$' extend-exclude = ''' ( __pycache__ | \.github ) ''' [tool.pylint] max-line-length = 120 disable = ["W0511"] [tool.isort] profile = 'black' multi_line_output = 3 line_length = 120 py_version = 38

petergtz

6ebfc4464bd5c41880f25299df25c3c1cd05b20c

b5ae49a256217f1cae5a45033e8e6bc84599e508

They both work. According to https://peps.python.org/pep-0503/#normalized-names, a dot gets replaced by a dash. Note also that we use `autogluon-tabular` already in other places in this project file. Also tested this locally. Both names work.

petergtz

py-why/dowhy

[Version Bump v0.9] Release notes and updated docstrings

This PR includes the release notes for v0.9 Signed-off-by: Amit Sharma <amit_sharma@live.com>

2022-12-04 10:24:21+00:00

2022-12-06 05:37:44+00:00

docs/source/code_repo.rst

Release notes ============= DoWhy is hosted on GitHub. You can browse the code in a html-friendly format `here <https://github.com/Microsoft/dowhy>`_. v0.7.1: Added Graph refuter. Support for dagitty graphs and external estimators -------------------------------------------------------------------------------------- * Graph refuter with conditional independence tests to check whether data conforms to the assumed causal graph * Better docs for estimators by adding the method-specific parameters directly in its own init method * Support use of custom external estimators * Consistent structure for init_params for dowhy and econml estimators * Add support for Dagitty graphs * Bug fixes for GLM model, causal model with no confounders, and hotel case-study notebook Thank you @EgorKraevTransferwise, @ae-foster, @anusha0409 for your contributions! v0.7: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Faster backdoor identification with support for minimal adjustment, maximal adjustment or exhaustive search. More test coverage for identification. * **[Major]** Added new functionality of causal discovery [Experimental]. DoWhy now supports discovery algorithms from external libraries like CDT. `[Example notebook] <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_discovery_example.ipynb>`_ * **[Major]** Implemented ID algorithm for causal identification. [Experimental] * Added friendly text-based interpretation for DoWhy's effect estimate. * Added a new estimation method, distance matching that relies on a distance metrics between inputs. * Heuristics to infer default parameters for refuters. * Inferring default strata automatically for propensity score stratification. * Added support for custom propensity models in propensity-based estimation methods. * Bug fixes for confidence intervals for linear regression. Better version of bootstrap method. * Allow effect estimation without need to refit the model for econml estimators Big thanks to @AndrewC19, @ha2trinh, @siddhanthaldar, and @vojavocni v0.6: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Placebo refuter also works for IV methods * **[Major]** Moved matplotlib to an optional dependency. Can be installed using `pip install dowhy[plotting]` * **[Major]** A new method for generating unobserved confounder for refutation * Update to align with EconML's new API * All refuters now support control and treatment values for continuous treatments * Better logging configuration * Dummyoutcomerefuter supports unobserved confounder A big thanks to @arshiaarya, @n8sty, @moprescu and @vojavocni v0.5-beta: Enhanced documentation and support for causal mediation ------------------------------------------------------------------- **Installation** * DoWhy can be installed on Conda now! **Code** * Support for identification by mediation formula * Support for the front-door criterion * Linear estimation methods for mediation * Generalized backdoor criterion implementation using paths and d-separation * Added GLM estimators, including logistic regression * New API for interpreting causal models, estimates and refuters. First interpreter by @ErikHambardzumyan visualizes how the distribution of confounder changes * Friendlier error messages for propensity score stratification estimator when there is not enough data in a bin * Enhancements to the dummy outcome refuter with machine learned components--now can simulate non-zero effects too. Ready for alpha testing **Docs** * New case studies using DoWhy on `hotel booking cancellations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/DoWhy-The%20Causal%20Story%20Behind%20Hotel%20Booking%20Cancellations.ipynb>`_ and `membership rewards programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ * New `notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_multiple_treatments.ipynb>`_ on using DoWhy+EconML for estimating effect of multiple treatments * A `tutorial <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/tutorial-causalinference-machinelearning-using-dowhy-econml.ipynb>`_ on causal inference using DoWhy and EconML * Better organization of docs and notebooks on the `documentation website <https://py-why.github.io/dowhy/>`_. **Community** * Created a `contributors page <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_ with guidelines for contributing * Added allcontributors bot so that new contributors can added just after their pull requests are merged A big thanks to @Tanmay-Kulkarni101, @ErikHambardzumyan, @Sid-darthvader for their contributions. v0.4-beta: Powerful refutations and better support for heterogeneous treatment effects -------------------------------------------------------------------------------------- * DummyOutcomeRefuter now includes machine learning functions to increase power of the refutation. * In addition to generating a random dummy outcome, now you can generate a dummyOutcome that is an arbitrary function of confounders but always independent of treatment, and then test whether the estimated treatment effect is zero. This is inspired by ideas from the T-learner. * We also provide default machine learning-based methods to estimate such a dummyOutcome based on confounders. Of course, you can specify any custom ML method. * Added a new BootstrapRefuter that simulates the issue of measurement error with confounders. Rather than a simple bootstrap, you can generate bootstrap samples with noise on the values of the confounders and check how sensitive the estimate is. * The refuter supports custom selection of the confounders to add noise to. * All refuters now provide confidence intervals and a significance value. * Better support for heterogeneous effect libraries like EconML and CausalML * All CausalML methods can be called directly from DoWhy, in addition to all methods from EconML. * [Change to naming scheme for estimators] To achieve a consistent naming scheme for estimators, we suggest to prepend internal dowhy estimators with the string "dowhy". For example, "backdoor.dowhy.propensity_score_matching". Not a breaking change, so you can keep using the old naming scheme too. * EconML-specific: Since EconML assumes that effect modifiers are a subset of confounders, a warning is issued if a user specifies effect modifiers outside of confounders and tries to use EconML methods. * CI and Standard errors: Added bootstrap-based confidence intervals and standard errors for all methods. For linear regression estimator, also implemented the corresponding parametric forms. * Convenience functions for getting confidence intervals, standard errors and conditional treatment effects (CATE), that can be called after fitting the estimator if needed * Better coverage for tests. Also, tests are now seeded with a random seed, so more dependable tests. Thanks to @Tanmay-Kulkarni101 and @Arshiaarya for their contributions! v0.2-alpha: CATE estimation and integration with EconML ------------------------------------------------------- This release includes many major updates: * (BREAKING CHANGE) The CausalModel import is now simpler: "from dowhy import CausalModel" * Multivariate treatments are now supported. * Conditional Average Treatment Effects (CATE) can be estimated for any subset of the data. Includes integration with EconML--any method from EconML can be called using DoWhy through the estimate_effect method (see example notebook). * Other than CATE, specific target estimands like ATT and ATC are also supported for many of the estimation methods. * For reproducibility, you can specify a random seed for all refutation methods. * Multiple bug fixes and updates to the documentation. Includes contributions from @j-chou, @ktmud, @jrfiedler, @shounak112358, @Lnk2past. Thank you all! v0.1.1-alpha: First release --------------------------- This is the first release of the library.

Release notes ============= DoWhy is hosted on GitHub. You can browse the code in a html-friendly format `here <https://github.com/Microsoft/dowhy>`_. v0.9: New functional API (preview), faster refutations, and better independence tests for GCMs ---------------------------------------------------------------------------------------------- December 5 2022 * Preview for the new functional API (see `notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_functional_api.ipynb>`_). The new API (in experimental stage) allows for a modular use of the different functionalities and includes separate fit and estimate methods for causal estimators. Please leave your feedback here. The old DoWhy API based on CausalModel should work as before. (@andresmor-ms) * Faster, better sensitivity analyses. * Many refutations now support joblib for parallel processing and show a progress bar (@astoeffelbauer, @yemaedahrav). * Non-linear sensitivity analysis [`Chernozhukov, Cinelli, Newey, Sharma & Syrgkanis (2021) <https://arxiv.org/abs/2112.13398>`_, `example notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/sensitivity_analysis_nonparametric_estimators.ipynb>`_] (@anusha0409) * E-value sensitivity analysis [`Ding & Vanderweele (2016) <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4820664/>`, `example notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/sensitivity_analysis_testing.ipynb>`_] (@jlgleason) * New API for unit change attribution (@kailashbuki) * New quality option `BEST` for auto-assignment of causal mechanisms, which uses the optional auto-ML library AutoGluon (@bloebp) * Better conditional independence tests through the causal-learn package (@bloebp) * Algorithms for computing efficient backdoor sets [`example notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_efficient_backdoor_example.ipynb>`_] (@esmucler) * Support for estimating controlled direct effect (@amit-sharma) * Support for multi-valued treatments for econml estimators (@EgorKraevTransferwise) * New PyData theme for documentation with new homepage, Getting started guide, revised User Guide and examples page (@petergtz) * A `contributing guide <https://github.com/py-why/dowhy/blob/main/docs/source/contributing/contributing-code.rst>`_ and simplified instructions for new contributors (@MichaelMarien) * Streamlined dev environment using Poetry for managing dependencies and project builds (@darthtrevino) * Bug fixes v0.8: GCM support and partial R2-based sensitivity analysis ------------------------------------------------------------- July 18 2022 A big thanks to @petergtz, @kailashbuki, and @bloebp for the GCM package and @anusha0409 for an implementation of partial R2 sensitivity analysis for linear models. * **Graphical Causal Models**: SCMs, root-cause analysis, attribution, what-if analysis, and more. * **Sensitivity Analysis**: Faster, more general partial-R2 based sensitivity analysis for linear models, based on `Cinelli & Hazlett (2020) <https://rss.onlinelibrary.wiley.com/doi/10.1111/rssb.12348>`_. * **New docs structure**: Updated docs structure including user and contributors' guide. Check out the `docs <https://py-why.github.io/dowhy/>`_. * Bug fixes **Contributors**: @amit-sharma, @anusha0409, @bloebp, @EgorKraevTransferwise, @elikling, @kailashbuki, @itsoum, @MichaelMarien, @petergtz, @ryanrussell v0.7.1: Added Graph refuter. Support for dagitty graphs and external estimators -------------------------------------------------------------------------------------- * Graph refuter with conditional independence tests to check whether data conforms to the assumed causal graph * Better docs for estimators by adding the method-specific parameters directly in its own init method * Support use of custom external estimators * Consistent structure for init_params for dowhy and econml estimators * Add support for Dagitty graphs * Bug fixes for GLM model, causal model with no confounders, and hotel case-study notebook Thank you @EgorKraevTransferwise, @ae-foster, @anusha0409 for your contributions! v0.7: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Faster backdoor identification with support for minimal adjustment, maximal adjustment or exhaustive search. More test coverage for identification. * **[Major]** Added new functionality of causal discovery [Experimental]. DoWhy now supports discovery algorithms from external libraries like CDT. `[Example notebook] <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_discovery_example.ipynb>`_ * **[Major]** Implemented ID algorithm for causal identification. [Experimental] * Added friendly text-based interpretation for DoWhy's effect estimate. * Added a new estimation method, distance matching that relies on a distance metrics between inputs. * Heuristics to infer default parameters for refuters. * Inferring default strata automatically for propensity score stratification. * Added support for custom propensity models in propensity-based estimation methods. * Bug fixes for confidence intervals for linear regression. Better version of bootstrap method. * Allow effect estimation without need to refit the model for econml estimators Big thanks to @AndrewC19, @ha2trinh, @siddhanthaldar, and @vojavocni v0.6: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Placebo refuter also works for IV methods * **[Major]** Moved matplotlib to an optional dependency. Can be installed using `pip install dowhy[plotting]` * **[Major]** A new method for generating unobserved confounder for refutation * Update to align with EconML's new API * All refuters now support control and treatment values for continuous treatments * Better logging configuration * Dummyoutcomerefuter supports unobserved confounder A big thanks to @arshiaarya, @n8sty, @moprescu and @vojavocni v0.5-beta: Enhanced documentation and support for causal mediation ------------------------------------------------------------------- **Installation** * DoWhy can be installed on Conda now! **Code** * Support for identification by mediation formula * Support for the front-door criterion * Linear estimation methods for mediation * Generalized backdoor criterion implementation using paths and d-separation * Added GLM estimators, including logistic regression * New API for interpreting causal models, estimates and refuters. First interpreter by @ErikHambardzumyan visualizes how the distribution of confounder changes * Friendlier error messages for propensity score stratification estimator when there is not enough data in a bin * Enhancements to the dummy outcome refuter with machine learned components--now can simulate non-zero effects too. Ready for alpha testing **Docs** * New case studies using DoWhy on `hotel booking cancellations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/DoWhy-The%20Causal%20Story%20Behind%20Hotel%20Booking%20Cancellations.ipynb>`_ and `membership rewards programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ * New `notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_multiple_treatments.ipynb>`_ on using DoWhy+EconML for estimating effect of multiple treatments * A `tutorial <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/tutorial-causalinference-machinelearning-using-dowhy-econml.ipynb>`_ on causal inference using DoWhy and EconML * Better organization of docs and notebooks on the `documentation website <https://py-why.github.io/dowhy/>`_. **Community** * Created a `contributors page <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_ with guidelines for contributing * Added allcontributors bot so that new contributors can added just after their pull requests are merged A big thanks to @Tanmay-Kulkarni101, @ErikHambardzumyan, @Sid-darthvader for their contributions. v0.4-beta: Powerful refutations and better support for heterogeneous treatment effects -------------------------------------------------------------------------------------- * DummyOutcomeRefuter now includes machine learning functions to increase power of the refutation. * In addition to generating a random dummy outcome, now you can generate a dummyOutcome that is an arbitrary function of confounders but always independent of treatment, and then test whether the estimated treatment effect is zero. This is inspired by ideas from the T-learner. * We also provide default machine learning-based methods to estimate such a dummyOutcome based on confounders. Of course, you can specify any custom ML method. * Added a new BootstrapRefuter that simulates the issue of measurement error with confounders. Rather than a simple bootstrap, you can generate bootstrap samples with noise on the values of the confounders and check how sensitive the estimate is. * The refuter supports custom selection of the confounders to add noise to. * All refuters now provide confidence intervals and a significance value. * Better support for heterogeneous effect libraries like EconML and CausalML * All CausalML methods can be called directly from DoWhy, in addition to all methods from EconML. * [Change to naming scheme for estimators] To achieve a consistent naming scheme for estimators, we suggest to prepend internal dowhy estimators with the string "dowhy". For example, "backdoor.dowhy.propensity_score_matching". Not a breaking change, so you can keep using the old naming scheme too. * EconML-specific: Since EconML assumes that effect modifiers are a subset of confounders, a warning is issued if a user specifies effect modifiers outside of confounders and tries to use EconML methods. * CI and Standard errors: Added bootstrap-based confidence intervals and standard errors for all methods. For linear regression estimator, also implemented the corresponding parametric forms. * Convenience functions for getting confidence intervals, standard errors and conditional treatment effects (CATE), that can be called after fitting the estimator if needed * Better coverage for tests. Also, tests are now seeded with a random seed, so more dependable tests. Thanks to @Tanmay-Kulkarni101 and @Arshiaarya for their contributions! v0.2-alpha: CATE estimation and integration with EconML ------------------------------------------------------- This release includes many major updates: * (BREAKING CHANGE) The CausalModel import is now simpler: "from dowhy import CausalModel" * Multivariate treatments are now supported. * Conditional Average Treatment Effects (CATE) can be estimated for any subset of the data. Includes integration with EconML--any method from EconML can be called using DoWhy through the estimate_effect method (see example notebook). * Other than CATE, specific target estimands like ATT and ATC are also supported for many of the estimation methods. * For reproducibility, you can specify a random seed for all refutation methods. * Multiple bug fixes and updates to the documentation. Includes contributions from @j-chou, @ktmud, @jrfiedler, @shounak112358, @Lnk2past. Thank you all! v0.1.1-alpha: First release --------------------------- This is the first release of the library.

amit-sharma

649b3c32a11ddff86e932c24b3551161ba5f5747

9e938f333ec5436697a4f48a7ebb0e63a39a0303

This should also list: ``` * New API for unit change attribution (@kailashbuki) * New quality option `BEST` for auto-assignment of causal mechanisms, which uses the optional auto-ML library AutoGluon (@bloebp) ```

petergtz

py-why/dowhy

[Version Bump v0.9] Release notes and updated docstrings

This PR includes the release notes for v0.9 Signed-off-by: Amit Sharma <amit_sharma@live.com>

2022-12-04 10:24:21+00:00

2022-12-06 05:37:44+00:00

docs/source/code_repo.rst

Release notes ============= DoWhy is hosted on GitHub. You can browse the code in a html-friendly format `here <https://github.com/Microsoft/dowhy>`_. v0.7.1: Added Graph refuter. Support for dagitty graphs and external estimators -------------------------------------------------------------------------------------- * Graph refuter with conditional independence tests to check whether data conforms to the assumed causal graph * Better docs for estimators by adding the method-specific parameters directly in its own init method * Support use of custom external estimators * Consistent structure for init_params for dowhy and econml estimators * Add support for Dagitty graphs * Bug fixes for GLM model, causal model with no confounders, and hotel case-study notebook Thank you @EgorKraevTransferwise, @ae-foster, @anusha0409 for your contributions! v0.7: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Faster backdoor identification with support for minimal adjustment, maximal adjustment or exhaustive search. More test coverage for identification. * **[Major]** Added new functionality of causal discovery [Experimental]. DoWhy now supports discovery algorithms from external libraries like CDT. `[Example notebook] <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_discovery_example.ipynb>`_ * **[Major]** Implemented ID algorithm for causal identification. [Experimental] * Added friendly text-based interpretation for DoWhy's effect estimate. * Added a new estimation method, distance matching that relies on a distance metrics between inputs. * Heuristics to infer default parameters for refuters. * Inferring default strata automatically for propensity score stratification. * Added support for custom propensity models in propensity-based estimation methods. * Bug fixes for confidence intervals for linear regression. Better version of bootstrap method. * Allow effect estimation without need to refit the model for econml estimators Big thanks to @AndrewC19, @ha2trinh, @siddhanthaldar, and @vojavocni v0.6: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Placebo refuter also works for IV methods * **[Major]** Moved matplotlib to an optional dependency. Can be installed using `pip install dowhy[plotting]` * **[Major]** A new method for generating unobserved confounder for refutation * Update to align with EconML's new API * All refuters now support control and treatment values for continuous treatments * Better logging configuration * Dummyoutcomerefuter supports unobserved confounder A big thanks to @arshiaarya, @n8sty, @moprescu and @vojavocni v0.5-beta: Enhanced documentation and support for causal mediation ------------------------------------------------------------------- **Installation** * DoWhy can be installed on Conda now! **Code** * Support for identification by mediation formula * Support for the front-door criterion * Linear estimation methods for mediation * Generalized backdoor criterion implementation using paths and d-separation * Added GLM estimators, including logistic regression * New API for interpreting causal models, estimates and refuters. First interpreter by @ErikHambardzumyan visualizes how the distribution of confounder changes * Friendlier error messages for propensity score stratification estimator when there is not enough data in a bin * Enhancements to the dummy outcome refuter with machine learned components--now can simulate non-zero effects too. Ready for alpha testing **Docs** * New case studies using DoWhy on `hotel booking cancellations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/DoWhy-The%20Causal%20Story%20Behind%20Hotel%20Booking%20Cancellations.ipynb>`_ and `membership rewards programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ * New `notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_multiple_treatments.ipynb>`_ on using DoWhy+EconML for estimating effect of multiple treatments * A `tutorial <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/tutorial-causalinference-machinelearning-using-dowhy-econml.ipynb>`_ on causal inference using DoWhy and EconML * Better organization of docs and notebooks on the `documentation website <https://py-why.github.io/dowhy/>`_. **Community** * Created a `contributors page <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_ with guidelines for contributing * Added allcontributors bot so that new contributors can added just after their pull requests are merged A big thanks to @Tanmay-Kulkarni101, @ErikHambardzumyan, @Sid-darthvader for their contributions. v0.4-beta: Powerful refutations and better support for heterogeneous treatment effects -------------------------------------------------------------------------------------- * DummyOutcomeRefuter now includes machine learning functions to increase power of the refutation. * In addition to generating a random dummy outcome, now you can generate a dummyOutcome that is an arbitrary function of confounders but always independent of treatment, and then test whether the estimated treatment effect is zero. This is inspired by ideas from the T-learner. * We also provide default machine learning-based methods to estimate such a dummyOutcome based on confounders. Of course, you can specify any custom ML method. * Added a new BootstrapRefuter that simulates the issue of measurement error with confounders. Rather than a simple bootstrap, you can generate bootstrap samples with noise on the values of the confounders and check how sensitive the estimate is. * The refuter supports custom selection of the confounders to add noise to. * All refuters now provide confidence intervals and a significance value. * Better support for heterogeneous effect libraries like EconML and CausalML * All CausalML methods can be called directly from DoWhy, in addition to all methods from EconML. * [Change to naming scheme for estimators] To achieve a consistent naming scheme for estimators, we suggest to prepend internal dowhy estimators with the string "dowhy". For example, "backdoor.dowhy.propensity_score_matching". Not a breaking change, so you can keep using the old naming scheme too. * EconML-specific: Since EconML assumes that effect modifiers are a subset of confounders, a warning is issued if a user specifies effect modifiers outside of confounders and tries to use EconML methods. * CI and Standard errors: Added bootstrap-based confidence intervals and standard errors for all methods. For linear regression estimator, also implemented the corresponding parametric forms. * Convenience functions for getting confidence intervals, standard errors and conditional treatment effects (CATE), that can be called after fitting the estimator if needed * Better coverage for tests. Also, tests are now seeded with a random seed, so more dependable tests. Thanks to @Tanmay-Kulkarni101 and @Arshiaarya for their contributions! v0.2-alpha: CATE estimation and integration with EconML ------------------------------------------------------- This release includes many major updates: * (BREAKING CHANGE) The CausalModel import is now simpler: "from dowhy import CausalModel" * Multivariate treatments are now supported. * Conditional Average Treatment Effects (CATE) can be estimated for any subset of the data. Includes integration with EconML--any method from EconML can be called using DoWhy through the estimate_effect method (see example notebook). * Other than CATE, specific target estimands like ATT and ATC are also supported for many of the estimation methods. * For reproducibility, you can specify a random seed for all refutation methods. * Multiple bug fixes and updates to the documentation. Includes contributions from @j-chou, @ktmud, @jrfiedler, @shounak112358, @Lnk2past. Thank you all! v0.1.1-alpha: First release --------------------------- This is the first release of the library.

Release notes ============= DoWhy is hosted on GitHub. You can browse the code in a html-friendly format `here <https://github.com/Microsoft/dowhy>`_. v0.9: New functional API (preview), faster refutations, and better independence tests for GCMs ---------------------------------------------------------------------------------------------- December 5 2022 * Preview for the new functional API (see `notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_functional_api.ipynb>`_). The new API (in experimental stage) allows for a modular use of the different functionalities and includes separate fit and estimate methods for causal estimators. Please leave your feedback here. The old DoWhy API based on CausalModel should work as before. (@andresmor-ms) * Faster, better sensitivity analyses. * Many refutations now support joblib for parallel processing and show a progress bar (@astoeffelbauer, @yemaedahrav). * Non-linear sensitivity analysis [`Chernozhukov, Cinelli, Newey, Sharma & Syrgkanis (2021) <https://arxiv.org/abs/2112.13398>`_, `example notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/sensitivity_analysis_nonparametric_estimators.ipynb>`_] (@anusha0409) * E-value sensitivity analysis [`Ding & Vanderweele (2016) <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4820664/>`, `example notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/sensitivity_analysis_testing.ipynb>`_] (@jlgleason) * New API for unit change attribution (@kailashbuki) * New quality option `BEST` for auto-assignment of causal mechanisms, which uses the optional auto-ML library AutoGluon (@bloebp) * Better conditional independence tests through the causal-learn package (@bloebp) * Algorithms for computing efficient backdoor sets [`example notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_efficient_backdoor_example.ipynb>`_] (@esmucler) * Support for estimating controlled direct effect (@amit-sharma) * Support for multi-valued treatments for econml estimators (@EgorKraevTransferwise) * New PyData theme for documentation with new homepage, Getting started guide, revised User Guide and examples page (@petergtz) * A `contributing guide <https://github.com/py-why/dowhy/blob/main/docs/source/contributing/contributing-code.rst>`_ and simplified instructions for new contributors (@MichaelMarien) * Streamlined dev environment using Poetry for managing dependencies and project builds (@darthtrevino) * Bug fixes v0.8: GCM support and partial R2-based sensitivity analysis ------------------------------------------------------------- July 18 2022 A big thanks to @petergtz, @kailashbuki, and @bloebp for the GCM package and @anusha0409 for an implementation of partial R2 sensitivity analysis for linear models. * **Graphical Causal Models**: SCMs, root-cause analysis, attribution, what-if analysis, and more. * **Sensitivity Analysis**: Faster, more general partial-R2 based sensitivity analysis for linear models, based on `Cinelli & Hazlett (2020) <https://rss.onlinelibrary.wiley.com/doi/10.1111/rssb.12348>`_. * **New docs structure**: Updated docs structure including user and contributors' guide. Check out the `docs <https://py-why.github.io/dowhy/>`_. * Bug fixes **Contributors**: @amit-sharma, @anusha0409, @bloebp, @EgorKraevTransferwise, @elikling, @kailashbuki, @itsoum, @MichaelMarien, @petergtz, @ryanrussell v0.7.1: Added Graph refuter. Support for dagitty graphs and external estimators -------------------------------------------------------------------------------------- * Graph refuter with conditional independence tests to check whether data conforms to the assumed causal graph * Better docs for estimators by adding the method-specific parameters directly in its own init method * Support use of custom external estimators * Consistent structure for init_params for dowhy and econml estimators * Add support for Dagitty graphs * Bug fixes for GLM model, causal model with no confounders, and hotel case-study notebook Thank you @EgorKraevTransferwise, @ae-foster, @anusha0409 for your contributions! v0.7: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Faster backdoor identification with support for minimal adjustment, maximal adjustment or exhaustive search. More test coverage for identification. * **[Major]** Added new functionality of causal discovery [Experimental]. DoWhy now supports discovery algorithms from external libraries like CDT. `[Example notebook] <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_discovery_example.ipynb>`_ * **[Major]** Implemented ID algorithm for causal identification. [Experimental] * Added friendly text-based interpretation for DoWhy's effect estimate. * Added a new estimation method, distance matching that relies on a distance metrics between inputs. * Heuristics to infer default parameters for refuters. * Inferring default strata automatically for propensity score stratification. * Added support for custom propensity models in propensity-based estimation methods. * Bug fixes for confidence intervals for linear regression. Better version of bootstrap method. * Allow effect estimation without need to refit the model for econml estimators Big thanks to @AndrewC19, @ha2trinh, @siddhanthaldar, and @vojavocni v0.6: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Placebo refuter also works for IV methods * **[Major]** Moved matplotlib to an optional dependency. Can be installed using `pip install dowhy[plotting]` * **[Major]** A new method for generating unobserved confounder for refutation * Update to align with EconML's new API * All refuters now support control and treatment values for continuous treatments * Better logging configuration * Dummyoutcomerefuter supports unobserved confounder A big thanks to @arshiaarya, @n8sty, @moprescu and @vojavocni v0.5-beta: Enhanced documentation and support for causal mediation ------------------------------------------------------------------- **Installation** * DoWhy can be installed on Conda now! **Code** * Support for identification by mediation formula * Support for the front-door criterion * Linear estimation methods for mediation * Generalized backdoor criterion implementation using paths and d-separation * Added GLM estimators, including logistic regression * New API for interpreting causal models, estimates and refuters. First interpreter by @ErikHambardzumyan visualizes how the distribution of confounder changes * Friendlier error messages for propensity score stratification estimator when there is not enough data in a bin * Enhancements to the dummy outcome refuter with machine learned components--now can simulate non-zero effects too. Ready for alpha testing **Docs** * New case studies using DoWhy on `hotel booking cancellations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/DoWhy-The%20Causal%20Story%20Behind%20Hotel%20Booking%20Cancellations.ipynb>`_ and `membership rewards programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ * New `notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_multiple_treatments.ipynb>`_ on using DoWhy+EconML for estimating effect of multiple treatments * A `tutorial <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/tutorial-causalinference-machinelearning-using-dowhy-econml.ipynb>`_ on causal inference using DoWhy and EconML * Better organization of docs and notebooks on the `documentation website <https://py-why.github.io/dowhy/>`_. **Community** * Created a `contributors page <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_ with guidelines for contributing * Added allcontributors bot so that new contributors can added just after their pull requests are merged A big thanks to @Tanmay-Kulkarni101, @ErikHambardzumyan, @Sid-darthvader for their contributions. v0.4-beta: Powerful refutations and better support for heterogeneous treatment effects -------------------------------------------------------------------------------------- * DummyOutcomeRefuter now includes machine learning functions to increase power of the refutation. * In addition to generating a random dummy outcome, now you can generate a dummyOutcome that is an arbitrary function of confounders but always independent of treatment, and then test whether the estimated treatment effect is zero. This is inspired by ideas from the T-learner. * We also provide default machine learning-based methods to estimate such a dummyOutcome based on confounders. Of course, you can specify any custom ML method. * Added a new BootstrapRefuter that simulates the issue of measurement error with confounders. Rather than a simple bootstrap, you can generate bootstrap samples with noise on the values of the confounders and check how sensitive the estimate is. * The refuter supports custom selection of the confounders to add noise to. * All refuters now provide confidence intervals and a significance value. * Better support for heterogeneous effect libraries like EconML and CausalML * All CausalML methods can be called directly from DoWhy, in addition to all methods from EconML. * [Change to naming scheme for estimators] To achieve a consistent naming scheme for estimators, we suggest to prepend internal dowhy estimators with the string "dowhy". For example, "backdoor.dowhy.propensity_score_matching". Not a breaking change, so you can keep using the old naming scheme too. * EconML-specific: Since EconML assumes that effect modifiers are a subset of confounders, a warning is issued if a user specifies effect modifiers outside of confounders and tries to use EconML methods. * CI and Standard errors: Added bootstrap-based confidence intervals and standard errors for all methods. For linear regression estimator, also implemented the corresponding parametric forms. * Convenience functions for getting confidence intervals, standard errors and conditional treatment effects (CATE), that can be called after fitting the estimator if needed * Better coverage for tests. Also, tests are now seeded with a random seed, so more dependable tests. Thanks to @Tanmay-Kulkarni101 and @Arshiaarya for their contributions! v0.2-alpha: CATE estimation and integration with EconML ------------------------------------------------------- This release includes many major updates: * (BREAKING CHANGE) The CausalModel import is now simpler: "from dowhy import CausalModel" * Multivariate treatments are now supported. * Conditional Average Treatment Effects (CATE) can be estimated for any subset of the data. Includes integration with EconML--any method from EconML can be called using DoWhy through the estimate_effect method (see example notebook). * Other than CATE, specific target estimands like ATT and ATC are also supported for many of the estimation methods. * For reproducibility, you can specify a random seed for all refutation methods. * Multiple bug fixes and updates to the documentation. Includes contributions from @j-chou, @ktmud, @jrfiedler, @shounak112358, @Lnk2past. Thank you all! v0.1.1-alpha: First release --------------------------- This is the first release of the library.

amit-sharma

649b3c32a11ddff86e932c24b3551161ba5f5747

9e938f333ec5436697a4f48a7ebb0e63a39a0303

> Also, you can now browse docs separately for different versions of DoWhy This was already available in the previous version, so you can probably remove that. How about: ``` * New PyData theme for documentation with new homepage, Getting started guide, revised User Guide and examples page (@petergtz) ``` The task-based view is not really ready yet. I've got only a draft of that, but it's not ready for sharing just yet.

petergtz

py-why/dowhy

[Version Bump v0.9] Release notes and updated docstrings

This PR includes the release notes for v0.9 Signed-off-by: Amit Sharma <amit_sharma@live.com>

2022-12-04 10:24:21+00:00

2022-12-06 05:37:44+00:00

docs/source/code_repo.rst

Release notes ============= DoWhy is hosted on GitHub. You can browse the code in a html-friendly format `here <https://github.com/Microsoft/dowhy>`_. v0.7.1: Added Graph refuter. Support for dagitty graphs and external estimators -------------------------------------------------------------------------------------- * Graph refuter with conditional independence tests to check whether data conforms to the assumed causal graph * Better docs for estimators by adding the method-specific parameters directly in its own init method * Support use of custom external estimators * Consistent structure for init_params for dowhy and econml estimators * Add support for Dagitty graphs * Bug fixes for GLM model, causal model with no confounders, and hotel case-study notebook Thank you @EgorKraevTransferwise, @ae-foster, @anusha0409 for your contributions! v0.7: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Faster backdoor identification with support for minimal adjustment, maximal adjustment or exhaustive search. More test coverage for identification. * **[Major]** Added new functionality of causal discovery [Experimental]. DoWhy now supports discovery algorithms from external libraries like CDT. `[Example notebook] <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_discovery_example.ipynb>`_ * **[Major]** Implemented ID algorithm for causal identification. [Experimental] * Added friendly text-based interpretation for DoWhy's effect estimate. * Added a new estimation method, distance matching that relies on a distance metrics between inputs. * Heuristics to infer default parameters for refuters. * Inferring default strata automatically for propensity score stratification. * Added support for custom propensity models in propensity-based estimation methods. * Bug fixes for confidence intervals for linear regression. Better version of bootstrap method. * Allow effect estimation without need to refit the model for econml estimators Big thanks to @AndrewC19, @ha2trinh, @siddhanthaldar, and @vojavocni v0.6: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Placebo refuter also works for IV methods * **[Major]** Moved matplotlib to an optional dependency. Can be installed using `pip install dowhy[plotting]` * **[Major]** A new method for generating unobserved confounder for refutation * Update to align with EconML's new API * All refuters now support control and treatment values for continuous treatments * Better logging configuration * Dummyoutcomerefuter supports unobserved confounder A big thanks to @arshiaarya, @n8sty, @moprescu and @vojavocni v0.5-beta: Enhanced documentation and support for causal mediation ------------------------------------------------------------------- **Installation** * DoWhy can be installed on Conda now! **Code** * Support for identification by mediation formula * Support for the front-door criterion * Linear estimation methods for mediation * Generalized backdoor criterion implementation using paths and d-separation * Added GLM estimators, including logistic regression * New API for interpreting causal models, estimates and refuters. First interpreter by @ErikHambardzumyan visualizes how the distribution of confounder changes * Friendlier error messages for propensity score stratification estimator when there is not enough data in a bin * Enhancements to the dummy outcome refuter with machine learned components--now can simulate non-zero effects too. Ready for alpha testing **Docs** * New case studies using DoWhy on `hotel booking cancellations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/DoWhy-The%20Causal%20Story%20Behind%20Hotel%20Booking%20Cancellations.ipynb>`_ and `membership rewards programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ * New `notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_multiple_treatments.ipynb>`_ on using DoWhy+EconML for estimating effect of multiple treatments * A `tutorial <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/tutorial-causalinference-machinelearning-using-dowhy-econml.ipynb>`_ on causal inference using DoWhy and EconML * Better organization of docs and notebooks on the `documentation website <https://py-why.github.io/dowhy/>`_. **Community** * Created a `contributors page <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_ with guidelines for contributing * Added allcontributors bot so that new contributors can added just after their pull requests are merged A big thanks to @Tanmay-Kulkarni101, @ErikHambardzumyan, @Sid-darthvader for their contributions. v0.4-beta: Powerful refutations and better support for heterogeneous treatment effects -------------------------------------------------------------------------------------- * DummyOutcomeRefuter now includes machine learning functions to increase power of the refutation. * In addition to generating a random dummy outcome, now you can generate a dummyOutcome that is an arbitrary function of confounders but always independent of treatment, and then test whether the estimated treatment effect is zero. This is inspired by ideas from the T-learner. * We also provide default machine learning-based methods to estimate such a dummyOutcome based on confounders. Of course, you can specify any custom ML method. * Added a new BootstrapRefuter that simulates the issue of measurement error with confounders. Rather than a simple bootstrap, you can generate bootstrap samples with noise on the values of the confounders and check how sensitive the estimate is. * The refuter supports custom selection of the confounders to add noise to. * All refuters now provide confidence intervals and a significance value. * Better support for heterogeneous effect libraries like EconML and CausalML * All CausalML methods can be called directly from DoWhy, in addition to all methods from EconML. * [Change to naming scheme for estimators] To achieve a consistent naming scheme for estimators, we suggest to prepend internal dowhy estimators with the string "dowhy". For example, "backdoor.dowhy.propensity_score_matching". Not a breaking change, so you can keep using the old naming scheme too. * EconML-specific: Since EconML assumes that effect modifiers are a subset of confounders, a warning is issued if a user specifies effect modifiers outside of confounders and tries to use EconML methods. * CI and Standard errors: Added bootstrap-based confidence intervals and standard errors for all methods. For linear regression estimator, also implemented the corresponding parametric forms. * Convenience functions for getting confidence intervals, standard errors and conditional treatment effects (CATE), that can be called after fitting the estimator if needed * Better coverage for tests. Also, tests are now seeded with a random seed, so more dependable tests. Thanks to @Tanmay-Kulkarni101 and @Arshiaarya for their contributions! v0.2-alpha: CATE estimation and integration with EconML ------------------------------------------------------- This release includes many major updates: * (BREAKING CHANGE) The CausalModel import is now simpler: "from dowhy import CausalModel" * Multivariate treatments are now supported. * Conditional Average Treatment Effects (CATE) can be estimated for any subset of the data. Includes integration with EconML--any method from EconML can be called using DoWhy through the estimate_effect method (see example notebook). * Other than CATE, specific target estimands like ATT and ATC are also supported for many of the estimation methods. * For reproducibility, you can specify a random seed for all refutation methods. * Multiple bug fixes and updates to the documentation. Includes contributions from @j-chou, @ktmud, @jrfiedler, @shounak112358, @Lnk2past. Thank you all! v0.1.1-alpha: First release --------------------------- This is the first release of the library.

Release notes ============= DoWhy is hosted on GitHub. You can browse the code in a html-friendly format `here <https://github.com/Microsoft/dowhy>`_. v0.9: New functional API (preview), faster refutations, and better independence tests for GCMs ---------------------------------------------------------------------------------------------- December 5 2022 * Preview for the new functional API (see `notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_functional_api.ipynb>`_). The new API (in experimental stage) allows for a modular use of the different functionalities and includes separate fit and estimate methods for causal estimators. Please leave your feedback here. The old DoWhy API based on CausalModel should work as before. (@andresmor-ms) * Faster, better sensitivity analyses. * Many refutations now support joblib for parallel processing and show a progress bar (@astoeffelbauer, @yemaedahrav). * Non-linear sensitivity analysis [`Chernozhukov, Cinelli, Newey, Sharma & Syrgkanis (2021) <https://arxiv.org/abs/2112.13398>`_, `example notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/sensitivity_analysis_nonparametric_estimators.ipynb>`_] (@anusha0409) * E-value sensitivity analysis [`Ding & Vanderweele (2016) <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4820664/>`, `example notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/sensitivity_analysis_testing.ipynb>`_] (@jlgleason) * New API for unit change attribution (@kailashbuki) * New quality option `BEST` for auto-assignment of causal mechanisms, which uses the optional auto-ML library AutoGluon (@bloebp) * Better conditional independence tests through the causal-learn package (@bloebp) * Algorithms for computing efficient backdoor sets [`example notebook <https://github.com/py-why/dowhy/blob/main/docs/source/example_notebooks/dowhy_efficient_backdoor_example.ipynb>`_] (@esmucler) * Support for estimating controlled direct effect (@amit-sharma) * Support for multi-valued treatments for econml estimators (@EgorKraevTransferwise) * New PyData theme for documentation with new homepage, Getting started guide, revised User Guide and examples page (@petergtz) * A `contributing guide <https://github.com/py-why/dowhy/blob/main/docs/source/contributing/contributing-code.rst>`_ and simplified instructions for new contributors (@MichaelMarien) * Streamlined dev environment using Poetry for managing dependencies and project builds (@darthtrevino) * Bug fixes v0.8: GCM support and partial R2-based sensitivity analysis ------------------------------------------------------------- July 18 2022 A big thanks to @petergtz, @kailashbuki, and @bloebp for the GCM package and @anusha0409 for an implementation of partial R2 sensitivity analysis for linear models. * **Graphical Causal Models**: SCMs, root-cause analysis, attribution, what-if analysis, and more. * **Sensitivity Analysis**: Faster, more general partial-R2 based sensitivity analysis for linear models, based on `Cinelli & Hazlett (2020) <https://rss.onlinelibrary.wiley.com/doi/10.1111/rssb.12348>`_. * **New docs structure**: Updated docs structure including user and contributors' guide. Check out the `docs <https://py-why.github.io/dowhy/>`_. * Bug fixes **Contributors**: @amit-sharma, @anusha0409, @bloebp, @EgorKraevTransferwise, @elikling, @kailashbuki, @itsoum, @MichaelMarien, @petergtz, @ryanrussell v0.7.1: Added Graph refuter. Support for dagitty graphs and external estimators -------------------------------------------------------------------------------------- * Graph refuter with conditional independence tests to check whether data conforms to the assumed causal graph * Better docs for estimators by adding the method-specific parameters directly in its own init method * Support use of custom external estimators * Consistent structure for init_params for dowhy and econml estimators * Add support for Dagitty graphs * Bug fixes for GLM model, causal model with no confounders, and hotel case-study notebook Thank you @EgorKraevTransferwise, @ae-foster, @anusha0409 for your contributions! v0.7: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Faster backdoor identification with support for minimal adjustment, maximal adjustment or exhaustive search. More test coverage for identification. * **[Major]** Added new functionality of causal discovery [Experimental]. DoWhy now supports discovery algorithms from external libraries like CDT. `[Example notebook] <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_causal_discovery_example.ipynb>`_ * **[Major]** Implemented ID algorithm for causal identification. [Experimental] * Added friendly text-based interpretation for DoWhy's effect estimate. * Added a new estimation method, distance matching that relies on a distance metrics between inputs. * Heuristics to infer default parameters for refuters. * Inferring default strata automatically for propensity score stratification. * Added support for custom propensity models in propensity-based estimation methods. * Bug fixes for confidence intervals for linear regression. Better version of bootstrap method. * Allow effect estimation without need to refit the model for econml estimators Big thanks to @AndrewC19, @ha2trinh, @siddhanthaldar, and @vojavocni v0.6: Better Refuters for unobserved confounders and placebo treatment ---------------------------------------------------------------------- * **[Major]** Placebo refuter also works for IV methods * **[Major]** Moved matplotlib to an optional dependency. Can be installed using `pip install dowhy[plotting]` * **[Major]** A new method for generating unobserved confounder for refutation * Update to align with EconML's new API * All refuters now support control and treatment values for continuous treatments * Better logging configuration * Dummyoutcomerefuter supports unobserved confounder A big thanks to @arshiaarya, @n8sty, @moprescu and @vojavocni v0.5-beta: Enhanced documentation and support for causal mediation ------------------------------------------------------------------- **Installation** * DoWhy can be installed on Conda now! **Code** * Support for identification by mediation formula * Support for the front-door criterion * Linear estimation methods for mediation * Generalized backdoor criterion implementation using paths and d-separation * Added GLM estimators, including logistic regression * New API for interpreting causal models, estimates and refuters. First interpreter by @ErikHambardzumyan visualizes how the distribution of confounder changes * Friendlier error messages for propensity score stratification estimator when there is not enough data in a bin * Enhancements to the dummy outcome refuter with machine learned components--now can simulate non-zero effects too. Ready for alpha testing **Docs** * New case studies using DoWhy on `hotel booking cancellations <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/DoWhy-The%20Causal%20Story%20Behind%20Hotel%20Booking%20Cancellations.ipynb>`_ and `membership rewards programs <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_example_effect_of_memberrewards_program.ipynb>`_ * New `notebook <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/dowhy_multiple_treatments.ipynb>`_ on using DoWhy+EconML for estimating effect of multiple treatments * A `tutorial <https://github.com/microsoft/dowhy/blob/main/docs/source/example_notebooks/tutorial-causalinference-machinelearning-using-dowhy-econml.ipynb>`_ on causal inference using DoWhy and EconML * Better organization of docs and notebooks on the `documentation website <https://py-why.github.io/dowhy/>`_. **Community** * Created a `contributors page <https://github.com/microsoft/dowhy/blob/main/CONTRIBUTING.md>`_ with guidelines for contributing * Added allcontributors bot so that new contributors can added just after their pull requests are merged A big thanks to @Tanmay-Kulkarni101, @ErikHambardzumyan, @Sid-darthvader for their contributions. v0.4-beta: Powerful refutations and better support for heterogeneous treatment effects -------------------------------------------------------------------------------------- * DummyOutcomeRefuter now includes machine learning functions to increase power of the refutation. * In addition to generating a random dummy outcome, now you can generate a dummyOutcome that is an arbitrary function of confounders but always independent of treatment, and then test whether the estimated treatment effect is zero. This is inspired by ideas from the T-learner. * We also provide default machine learning-based methods to estimate such a dummyOutcome based on confounders. Of course, you can specify any custom ML method. * Added a new BootstrapRefuter that simulates the issue of measurement error with confounders. Rather than a simple bootstrap, you can generate bootstrap samples with noise on the values of the confounders and check how sensitive the estimate is. * The refuter supports custom selection of the confounders to add noise to. * All refuters now provide confidence intervals and a significance value. * Better support for heterogeneous effect libraries like EconML and CausalML * All CausalML methods can be called directly from DoWhy, in addition to all methods from EconML. * [Change to naming scheme for estimators] To achieve a consistent naming scheme for estimators, we suggest to prepend internal dowhy estimators with the string "dowhy". For example, "backdoor.dowhy.propensity_score_matching". Not a breaking change, so you can keep using the old naming scheme too. * EconML-specific: Since EconML assumes that effect modifiers are a subset of confounders, a warning is issued if a user specifies effect modifiers outside of confounders and tries to use EconML methods. * CI and Standard errors: Added bootstrap-based confidence intervals and standard errors for all methods. For linear regression estimator, also implemented the corresponding parametric forms. * Convenience functions for getting confidence intervals, standard errors and conditional treatment effects (CATE), that can be called after fitting the estimator if needed * Better coverage for tests. Also, tests are now seeded with a random seed, so more dependable tests. Thanks to @Tanmay-Kulkarni101 and @Arshiaarya for their contributions! v0.2-alpha: CATE estimation and integration with EconML ------------------------------------------------------- This release includes many major updates: * (BREAKING CHANGE) The CausalModel import is now simpler: "from dowhy import CausalModel" * Multivariate treatments are now supported. * Conditional Average Treatment Effects (CATE) can be estimated for any subset of the data. Includes integration with EconML--any method from EconML can be called using DoWhy through the estimate_effect method (see example notebook). * Other than CATE, specific target estimands like ATT and ATC are also supported for many of the estimation methods. * For reproducibility, you can specify a random seed for all refutation methods. * Multiple bug fixes and updates to the documentation. Includes contributions from @j-chou, @ktmud, @jrfiedler, @shounak112358, @Lnk2past. Thank you all! v0.1.1-alpha: First release --------------------------- This is the first release of the library.

amit-sharma

649b3c32a11ddff86e932c24b3551161ba5f5747

9e938f333ec5436697a4f48a7ebb0e63a39a0303

Got it, making those changes.

amit-sharma

py-why/dowhy

[Version Bump v0.9] Release notes and updated docstrings

This PR includes the release notes for v0.9 Signed-off-by: Amit Sharma <amit_sharma@live.com>

2022-12-04 10:24:21+00:00

2022-12-06 05:37:44+00:00

docs/source/dowhy.rst

API reference ============= Subpackages ----------- .. toctree:: :maxdepth: 4 dowhy.api dowhy.causal_estimators dowhy.causal_identifiers dowhy.causal_refuters dowhy.data_transformers dowhy.do_samplers dowhy.gcm dowhy.graph_learners dowhy.interpreters dowhy.utils Submodules ---------- dowhy.causal\_estimator module ------------------------------ .. automodule:: dowhy.causal_estimator :members: :undoc-members: :show-inheritance: dowhy.causal\_graph module -------------------------- .. automodule:: dowhy.causal_graph :members: :undoc-members: :show-inheritance: dowhy.causal\_identifier module ------------------------------- .. automodule:: dowhy.causal_identifier :members: :undoc-members: :show-inheritance: dowhy.causal\_model module -------------------------- .. automodule:: dowhy.causal_model :members: :undoc-members: :show-inheritance: dowhy.causal\_refuter module ---------------------------- .. automodule:: dowhy.causal_refuter :members: :undoc-members: :show-inheritance: dowhy.data\_transformer module ------------------------------ .. automodule:: dowhy.data_transformer :members: :undoc-members: :show-inheritance: dowhy.datasets module --------------------- .. automodule:: dowhy.datasets :members: :undoc-members: :show-inheritance: dowhy.do\_sampler module ------------------------ .. automodule:: dowhy.do_sampler :members: :undoc-members: :show-inheritance: dowhy.graph\_learner module --------------------------- .. automodule:: dowhy.graph_learner :members: :undoc-members: :show-inheritance: dowhy.interpreter module ------------------------ .. automodule:: dowhy.interpreter :members: :undoc-members: :show-inheritance: dowhy.plotter module -------------------- .. automodule:: dowhy.plotter :members: :undoc-members: :show-inheritance: Module contents --------------- .. automodule:: dowhy :members: :undoc-members: :show-inheritance:

API reference ============= Subpackages ----------- .. toctree:: :maxdepth: 4 dowhy.api dowhy.causal_estimators dowhy.causal_identifier dowhy.causal_refuters dowhy.data_transformers dowhy.do_samplers dowhy.gcm dowhy.graph_learners dowhy.interpreters dowhy.utils Submodules ---------- dowhy.causal\_estimator module ------------------------------ .. automodule:: dowhy.causal_estimator :members: :undoc-members: :show-inheritance: dowhy.causal\_graph module -------------------------- .. automodule:: dowhy.causal_graph :members: :undoc-members: :show-inheritance: dowhy.causal\_model module -------------------------- .. automodule:: dowhy.causal_model :members: :undoc-members: :show-inheritance: dowhy.causal\_refuter module ---------------------------- .. automodule:: dowhy.causal_refuter :members: :undoc-members: :show-inheritance: dowhy.data\_transformer module ------------------------------ .. automodule:: dowhy.data_transformer :members: :undoc-members: :show-inheritance: dowhy.datasets module --------------------- .. automodule:: dowhy.datasets :members: :undoc-members: :show-inheritance: dowhy.do\_sampler module ------------------------ .. automodule:: dowhy.do_sampler :members: :undoc-members: :show-inheritance: dowhy.graph\_learner module --------------------------- .. automodule:: dowhy.graph_learner :members: :undoc-members: :show-inheritance: dowhy.interpreter module ------------------------ .. automodule:: dowhy.interpreter :members: :undoc-members: :show-inheritance: dowhy.plotter module -------------------- .. automodule:: dowhy.plotter :members: :undoc-members: :show-inheritance: Module contents --------------- .. automodule:: dowhy :members: :undoc-members: :show-inheritance:

amit-sharma

649b3c32a11ddff86e932c24b3551161ba5f5747

9e938f333ec5436697a4f48a7ebb0e63a39a0303

Did you change this on purpose? Typically, this part is called the "API Reference", so I would assume users would look for that when they search for documentation on DoWhy's API.

petergtz

py-why/dowhy

[Version Bump v0.9] Release notes and updated docstrings

This PR includes the release notes for v0.9 Signed-off-by: Amit Sharma <amit_sharma@live.com>

2022-12-04 10:24:21+00:00

2022-12-06 05:37:44+00:00

docs/source/dowhy.rst

API reference ============= Subpackages ----------- .. toctree:: :maxdepth: 4 dowhy.api dowhy.causal_estimators dowhy.causal_identifiers dowhy.causal_refuters dowhy.data_transformers dowhy.do_samplers dowhy.gcm dowhy.graph_learners dowhy.interpreters dowhy.utils Submodules ---------- dowhy.causal\_estimator module ------------------------------ .. automodule:: dowhy.causal_estimator :members: :undoc-members: :show-inheritance: dowhy.causal\_graph module -------------------------- .. automodule:: dowhy.causal_graph :members: :undoc-members: :show-inheritance: dowhy.causal\_identifier module ------------------------------- .. automodule:: dowhy.causal_identifier :members: :undoc-members: :show-inheritance: dowhy.causal\_model module -------------------------- .. automodule:: dowhy.causal_model :members: :undoc-members: :show-inheritance: dowhy.causal\_refuter module ---------------------------- .. automodule:: dowhy.causal_refuter :members: :undoc-members: :show-inheritance: dowhy.data\_transformer module ------------------------------ .. automodule:: dowhy.data_transformer :members: :undoc-members: :show-inheritance: dowhy.datasets module --------------------- .. automodule:: dowhy.datasets :members: :undoc-members: :show-inheritance: dowhy.do\_sampler module ------------------------ .. automodule:: dowhy.do_sampler :members: :undoc-members: :show-inheritance: dowhy.graph\_learner module --------------------------- .. automodule:: dowhy.graph_learner :members: :undoc-members: :show-inheritance: dowhy.interpreter module ------------------------ .. automodule:: dowhy.interpreter :members: :undoc-members: :show-inheritance: dowhy.plotter module -------------------- .. automodule:: dowhy.plotter :members: :undoc-members: :show-inheritance: Module contents --------------- .. automodule:: dowhy :members: :undoc-members: :show-inheritance:

API reference ============= Subpackages ----------- .. toctree:: :maxdepth: 4 dowhy.api dowhy.causal_estimators dowhy.causal_identifier dowhy.causal_refuters dowhy.data_transformers dowhy.do_samplers dowhy.gcm dowhy.graph_learners dowhy.interpreters dowhy.utils Submodules ---------- dowhy.causal\_estimator module ------------------------------ .. automodule:: dowhy.causal_estimator :members: :undoc-members: :show-inheritance: dowhy.causal\_graph module -------------------------- .. automodule:: dowhy.causal_graph :members: :undoc-members: :show-inheritance: dowhy.causal\_model module -------------------------- .. automodule:: dowhy.causal_model :members: :undoc-members: :show-inheritance: dowhy.causal\_refuter module ---------------------------- .. automodule:: dowhy.causal_refuter :members: :undoc-members: :show-inheritance: dowhy.data\_transformer module ------------------------------ .. automodule:: dowhy.data_transformer :members: :undoc-members: :show-inheritance: dowhy.datasets module --------------------- .. automodule:: dowhy.datasets :members: :undoc-members: :show-inheritance: dowhy.do\_sampler module ------------------------ .. automodule:: dowhy.do_sampler :members: :undoc-members: :show-inheritance: dowhy.graph\_learner module --------------------------- .. automodule:: dowhy.graph_learner :members: :undoc-members: :show-inheritance: dowhy.interpreter module ------------------------ .. automodule:: dowhy.interpreter :members: :undoc-members: :show-inheritance: dowhy.plotter module -------------------- .. automodule:: dowhy.plotter :members: :undoc-members: :show-inheritance: Module contents --------------- .. automodule:: dowhy :members: :undoc-members: :show-inheritance:

amit-sharma

649b3c32a11ddff86e932c24b3551161ba5f5747

9e938f333ec5436697a4f48a7ebb0e63a39a0303

No, let me revert it back.

amit-sharma

py-why/dowhy

An attempt at a DCO-compliant version of multivalue treatment PR

Signed-off-by: Egor Kraev egor.kraev@wise.com

2022-11-21 08:19:21+00:00

2022-11-24 06:17:03+00:00

dowhy/causal_estimators/econml.py

import inspect from importlib import import_module import econml import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X n_target_units = n_samples if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] n_target_units = X_test.shape[0] # Changing shape to a list for a singleton value if type(self._control_value) is not list: self._control_value = [self._control_value] if type(self._treatment_value) is not list: self._treatment_value = [self._treatment_value] T0_test = np.repeat([self._control_value], n_target_units, axis=0) T1_test = np.repeat([self._treatment_value], n_target_units, axis=0) est = self.estimator.effect(X_test, T0=T0_test, T1=T1_test) ate = np.mean(est) self.effect_intervals = None if self._confidence_intervals: self.effect_intervals = self.estimator.effect_interval( X_test, T0=T0_test, T1=T1_test, alpha=1 - self.confidence_level ) estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect(df[self._effect_modifier_names].values, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect_inference(df[self._effect_modifier_names].values, *args, **kwargs)

import inspect from importlib import import_module from typing import Callable import numpy as np import pandas as pd from numpy.distutils.misc_util import is_sequence from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] # Changing shape to a list for a singleton value self._treatment_value = parse_state(self._treatment_value) est = self.effect(X_test) ate = np.mean(est, axis=0) # one value per treatment value if len(ate) == 1: ate = ate[0] if self._confidence_intervals: self.effect_intervals = self.effect_interval(X_test) else: self.effect_intervals = None estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def apply_multitreatment(self, df: pd.DataFrame, fun: Callable, *args, **kwargs): ests = [] assert not isinstance(self._treatment_value, str) assert is_sequence(self._treatment_value) if df is None: filtered_df = None else: filtered_df = df[self._effect_modifier_names].values for tv in self._treatment_value: ests.append( fun( filtered_df, T0=self._control_value, T1=tv, *args, **kwargs, ) ) est = np.stack(ests, axis=1) return est def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise estimated treatment effect, output shape n_units x n_treatment_values (not counting control) :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_fun, *args, **kwargs) def effect_interval(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise confidence intervals for the estimated treatment effect :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_interval_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_interval( filtered_df, T0=T0, T1=T1, alpha=1 - self.confidence_level, *args, **kwargs ) return self.apply_multitreatment(df, effect_interval_fun, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs): """ Inference (uncertainty) results produced by the underlying EconML estimator :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_inference_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_inference(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_inference_fun, *args, **kwargs) def effect_tt(self, df: pd.DataFrame, *args, **kwargs): """ Effect of the actual treatment that was applied to each unit ("effect of Treatment on the Treated") :param df: Features of the units to evaluate :param args: passed through to estimator.effect() :param kwargs: passed through to estimator.effect() """ eff = self.effect(df, *args, **kwargs).reshape((len(df), len(self._treatment_value))) out = np.zeros(len(df)) treatment_value = parse_state(self._treatment_value) treatment_name = parse_state(self._treatment_name)[0] eff = np.reshape(eff, (len(df), len(treatment_value))) # For each unit, return the estimated effect of the treatment value # that was actually applied to the unit for c, col in enumerate(treatment_value): out[df[treatment_name] == col] = eff[df[treatment_name] == col, c] return pd.Series(data=out, index=df.index)

EgorKraevTransferwise

f83a276393f7f89e8c7991e5750c2f1095127e04

6cf8366c48b5f010952c14f615585a41cd37c3bf

what does tt stand for? true treatment?

amit-sharma

py-why/dowhy

An attempt at a DCO-compliant version of multivalue treatment PR

Signed-off-by: Egor Kraev egor.kraev@wise.com

2022-11-21 08:19:21+00:00

2022-11-24 06:17:03+00:00

dowhy/causal_estimators/econml.py

import inspect from importlib import import_module import econml import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X n_target_units = n_samples if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] n_target_units = X_test.shape[0] # Changing shape to a list for a singleton value if type(self._control_value) is not list: self._control_value = [self._control_value] if type(self._treatment_value) is not list: self._treatment_value = [self._treatment_value] T0_test = np.repeat([self._control_value], n_target_units, axis=0) T1_test = np.repeat([self._treatment_value], n_target_units, axis=0) est = self.estimator.effect(X_test, T0=T0_test, T1=T1_test) ate = np.mean(est) self.effect_intervals = None if self._confidence_intervals: self.effect_intervals = self.estimator.effect_interval( X_test, T0=T0_test, T1=T1_test, alpha=1 - self.confidence_level ) estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect(df[self._effect_modifier_names].values, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect_inference(df[self._effect_modifier_names].values, *args, **kwargs)

import inspect from importlib import import_module from typing import Callable import numpy as np import pandas as pd from numpy.distutils.misc_util import is_sequence from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] # Changing shape to a list for a singleton value self._treatment_value = parse_state(self._treatment_value) est = self.effect(X_test) ate = np.mean(est, axis=0) # one value per treatment value if len(ate) == 1: ate = ate[0] if self._confidence_intervals: self.effect_intervals = self.effect_interval(X_test) else: self.effect_intervals = None estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def apply_multitreatment(self, df: pd.DataFrame, fun: Callable, *args, **kwargs): ests = [] assert not isinstance(self._treatment_value, str) assert is_sequence(self._treatment_value) if df is None: filtered_df = None else: filtered_df = df[self._effect_modifier_names].values for tv in self._treatment_value: ests.append( fun( filtered_df, T0=self._control_value, T1=tv, *args, **kwargs, ) ) est = np.stack(ests, axis=1) return est def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise estimated treatment effect, output shape n_units x n_treatment_values (not counting control) :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_fun, *args, **kwargs) def effect_interval(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise confidence intervals for the estimated treatment effect :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_interval_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_interval( filtered_df, T0=T0, T1=T1, alpha=1 - self.confidence_level, *args, **kwargs ) return self.apply_multitreatment(df, effect_interval_fun, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs): """ Inference (uncertainty) results produced by the underlying EconML estimator :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_inference_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_inference(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_inference_fun, *args, **kwargs) def effect_tt(self, df: pd.DataFrame, *args, **kwargs): """ Effect of the actual treatment that was applied to each unit ("effect of Treatment on the Treated") :param df: Features of the units to evaluate :param args: passed through to estimator.effect() :param kwargs: passed through to estimator.effect() """ eff = self.effect(df, *args, **kwargs).reshape((len(df), len(self._treatment_value))) out = np.zeros(len(df)) treatment_value = parse_state(self._treatment_value) treatment_name = parse_state(self._treatment_name)[0] eff = np.reshape(eff, (len(df), len(treatment_value))) # For each unit, return the estimated effect of the treatment value # that was actually applied to the unit for c, col in enumerate(treatment_value): out[df[treatment_name] == col] = eff[df[treatment_name] == col, c] return pd.Series(data=out, index=df.index)

EgorKraevTransferwise

f83a276393f7f89e8c7991e5750c2f1095127e04

6cf8366c48b5f010952c14f615585a41cd37c3bf

I did not understand what this loop does? An inline comment will help.

amit-sharma

py-why/dowhy

An attempt at a DCO-compliant version of multivalue treatment PR

Signed-off-by: Egor Kraev egor.kraev@wise.com

2022-11-21 08:19:21+00:00

2022-11-24 06:17:03+00:00

dowhy/causal_estimators/econml.py

import inspect from importlib import import_module import econml import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X n_target_units = n_samples if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] n_target_units = X_test.shape[0] # Changing shape to a list for a singleton value if type(self._control_value) is not list: self._control_value = [self._control_value] if type(self._treatment_value) is not list: self._treatment_value = [self._treatment_value] T0_test = np.repeat([self._control_value], n_target_units, axis=0) T1_test = np.repeat([self._treatment_value], n_target_units, axis=0) est = self.estimator.effect(X_test, T0=T0_test, T1=T1_test) ate = np.mean(est) self.effect_intervals = None if self._confidence_intervals: self.effect_intervals = self.estimator.effect_interval( X_test, T0=T0_test, T1=T1_test, alpha=1 - self.confidence_level ) estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect(df[self._effect_modifier_names].values, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect_inference(df[self._effect_modifier_names].values, *args, **kwargs)

import inspect from importlib import import_module from typing import Callable import numpy as np import pandas as pd from numpy.distutils.misc_util import is_sequence from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] # Changing shape to a list for a singleton value self._treatment_value = parse_state(self._treatment_value) est = self.effect(X_test) ate = np.mean(est, axis=0) # one value per treatment value if len(ate) == 1: ate = ate[0] if self._confidence_intervals: self.effect_intervals = self.effect_interval(X_test) else: self.effect_intervals = None estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def apply_multitreatment(self, df: pd.DataFrame, fun: Callable, *args, **kwargs): ests = [] assert not isinstance(self._treatment_value, str) assert is_sequence(self._treatment_value) if df is None: filtered_df = None else: filtered_df = df[self._effect_modifier_names].values for tv in self._treatment_value: ests.append( fun( filtered_df, T0=self._control_value, T1=tv, *args, **kwargs, ) ) est = np.stack(ests, axis=1) return est def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise estimated treatment effect, output shape n_units x n_treatment_values (not counting control) :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_fun, *args, **kwargs) def effect_interval(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise confidence intervals for the estimated treatment effect :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_interval_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_interval( filtered_df, T0=T0, T1=T1, alpha=1 - self.confidence_level, *args, **kwargs ) return self.apply_multitreatment(df, effect_interval_fun, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs): """ Inference (uncertainty) results produced by the underlying EconML estimator :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_inference_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_inference(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_inference_fun, *args, **kwargs) def effect_tt(self, df: pd.DataFrame, *args, **kwargs): """ Effect of the actual treatment that was applied to each unit ("effect of Treatment on the Treated") :param df: Features of the units to evaluate :param args: passed through to estimator.effect() :param kwargs: passed through to estimator.effect() """ eff = self.effect(df, *args, **kwargs).reshape((len(df), len(self._treatment_value))) out = np.zeros(len(df)) treatment_value = parse_state(self._treatment_value) treatment_name = parse_state(self._treatment_name)[0] eff = np.reshape(eff, (len(df), len(treatment_value))) # For each unit, return the estimated effect of the treatment value # that was actually applied to the unit for c, col in enumerate(treatment_value): out[df[treatment_name] == col] = eff[df[treatment_name] == col, c] return pd.Series(data=out, index=df.index)

EgorKraevTransferwise

f83a276393f7f89e8c7991e5750c2f1095127e04

6cf8366c48b5f010952c14f615585a41cd37c3bf

will it possible to add a docstring for these methods? It will be good to add a docstring to the the methods we expect people to access. In the past, we were not so consistent, but this will be a good practice.

amit-sharma

py-why/dowhy

An attempt at a DCO-compliant version of multivalue treatment PR

Signed-off-by: Egor Kraev egor.kraev@wise.com

2022-11-21 08:19:21+00:00

2022-11-24 06:17:03+00:00

dowhy/causal_estimators/econml.py

import inspect from importlib import import_module import econml import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X n_target_units = n_samples if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] n_target_units = X_test.shape[0] # Changing shape to a list for a singleton value if type(self._control_value) is not list: self._control_value = [self._control_value] if type(self._treatment_value) is not list: self._treatment_value = [self._treatment_value] T0_test = np.repeat([self._control_value], n_target_units, axis=0) T1_test = np.repeat([self._treatment_value], n_target_units, axis=0) est = self.estimator.effect(X_test, T0=T0_test, T1=T1_test) ate = np.mean(est) self.effect_intervals = None if self._confidence_intervals: self.effect_intervals = self.estimator.effect_interval( X_test, T0=T0_test, T1=T1_test, alpha=1 - self.confidence_level ) estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect(df[self._effect_modifier_names].values, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect_inference(df[self._effect_modifier_names].values, *args, **kwargs)

import inspect from importlib import import_module from typing import Callable import numpy as np import pandas as pd from numpy.distutils.misc_util import is_sequence from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] # Changing shape to a list for a singleton value self._treatment_value = parse_state(self._treatment_value) est = self.effect(X_test) ate = np.mean(est, axis=0) # one value per treatment value if len(ate) == 1: ate = ate[0] if self._confidence_intervals: self.effect_intervals = self.effect_interval(X_test) else: self.effect_intervals = None estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def apply_multitreatment(self, df: pd.DataFrame, fun: Callable, *args, **kwargs): ests = [] assert not isinstance(self._treatment_value, str) assert is_sequence(self._treatment_value) if df is None: filtered_df = None else: filtered_df = df[self._effect_modifier_names].values for tv in self._treatment_value: ests.append( fun( filtered_df, T0=self._control_value, T1=tv, *args, **kwargs, ) ) est = np.stack(ests, axis=1) return est def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise estimated treatment effect, output shape n_units x n_treatment_values (not counting control) :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_fun, *args, **kwargs) def effect_interval(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise confidence intervals for the estimated treatment effect :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_interval_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_interval( filtered_df, T0=T0, T1=T1, alpha=1 - self.confidence_level, *args, **kwargs ) return self.apply_multitreatment(df, effect_interval_fun, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs): """ Inference (uncertainty) results produced by the underlying EconML estimator :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_inference_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_inference(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_inference_fun, *args, **kwargs) def effect_tt(self, df: pd.DataFrame, *args, **kwargs): """ Effect of the actual treatment that was applied to each unit ("effect of Treatment on the Treated") :param df: Features of the units to evaluate :param args: passed through to estimator.effect() :param kwargs: passed through to estimator.effect() """ eff = self.effect(df, *args, **kwargs).reshape((len(df), len(self._treatment_value))) out = np.zeros(len(df)) treatment_value = parse_state(self._treatment_value) treatment_name = parse_state(self._treatment_name)[0] eff = np.reshape(eff, (len(df), len(treatment_value))) # For each unit, return the estimated effect of the treatment value # that was actually applied to the unit for c, col in enumerate(treatment_value): out[df[treatment_name] == col] = eff[df[treatment_name] == col, c] return pd.Series(data=out, index=df.index)

EgorKraevTransferwise

f83a276393f7f89e8c7991e5750c2f1095127e04

6cf8366c48b5f010952c14f615585a41cd37c3bf

Adding a line in docstring to clarify

EgorKraevTransferwise

py-why/dowhy

An attempt at a DCO-compliant version of multivalue treatment PR

Signed-off-by: Egor Kraev egor.kraev@wise.com

2022-11-21 08:19:21+00:00

2022-11-24 06:17:03+00:00

dowhy/causal_estimators/econml.py

import inspect from importlib import import_module import econml import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X n_target_units = n_samples if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] n_target_units = X_test.shape[0] # Changing shape to a list for a singleton value if type(self._control_value) is not list: self._control_value = [self._control_value] if type(self._treatment_value) is not list: self._treatment_value = [self._treatment_value] T0_test = np.repeat([self._control_value], n_target_units, axis=0) T1_test = np.repeat([self._treatment_value], n_target_units, axis=0) est = self.estimator.effect(X_test, T0=T0_test, T1=T1_test) ate = np.mean(est) self.effect_intervals = None if self._confidence_intervals: self.effect_intervals = self.estimator.effect_interval( X_test, T0=T0_test, T1=T1_test, alpha=1 - self.confidence_level ) estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect(df[self._effect_modifier_names].values, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect_inference(df[self._effect_modifier_names].values, *args, **kwargs)

import inspect from importlib import import_module from typing import Callable import numpy as np import pandas as pd from numpy.distutils.misc_util import is_sequence from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] # Changing shape to a list for a singleton value self._treatment_value = parse_state(self._treatment_value) est = self.effect(X_test) ate = np.mean(est, axis=0) # one value per treatment value if len(ate) == 1: ate = ate[0] if self._confidence_intervals: self.effect_intervals = self.effect_interval(X_test) else: self.effect_intervals = None estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def apply_multitreatment(self, df: pd.DataFrame, fun: Callable, *args, **kwargs): ests = [] assert not isinstance(self._treatment_value, str) assert is_sequence(self._treatment_value) if df is None: filtered_df = None else: filtered_df = df[self._effect_modifier_names].values for tv in self._treatment_value: ests.append( fun( filtered_df, T0=self._control_value, T1=tv, *args, **kwargs, ) ) est = np.stack(ests, axis=1) return est def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise estimated treatment effect, output shape n_units x n_treatment_values (not counting control) :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_fun, *args, **kwargs) def effect_interval(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise confidence intervals for the estimated treatment effect :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_interval_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_interval( filtered_df, T0=T0, T1=T1, alpha=1 - self.confidence_level, *args, **kwargs ) return self.apply_multitreatment(df, effect_interval_fun, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs): """ Inference (uncertainty) results produced by the underlying EconML estimator :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_inference_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_inference(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_inference_fun, *args, **kwargs) def effect_tt(self, df: pd.DataFrame, *args, **kwargs): """ Effect of the actual treatment that was applied to each unit ("effect of Treatment on the Treated") :param df: Features of the units to evaluate :param args: passed through to estimator.effect() :param kwargs: passed through to estimator.effect() """ eff = self.effect(df, *args, **kwargs).reshape((len(df), len(self._treatment_value))) out = np.zeros(len(df)) treatment_value = parse_state(self._treatment_value) treatment_name = parse_state(self._treatment_name)[0] eff = np.reshape(eff, (len(df), len(treatment_value))) # For each unit, return the estimated effect of the treatment value # that was actually applied to the unit for c, col in enumerate(treatment_value): out[df[treatment_name] == col] = eff[df[treatment_name] == col, c] return pd.Series(data=out, index=df.index)

EgorKraevTransferwise

f83a276393f7f89e8c7991e5750c2f1095127e04

6cf8366c48b5f010952c14f615585a41cd37c3bf

Adding

EgorKraevTransferwise

py-why/dowhy

An attempt at a DCO-compliant version of multivalue treatment PR

Signed-off-by: Egor Kraev egor.kraev@wise.com

2022-11-21 08:19:21+00:00

2022-11-24 06:17:03+00:00

dowhy/causal_estimators/econml.py

import inspect from importlib import import_module import econml import numpy as np import pandas as pd from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X n_target_units = n_samples if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] n_target_units = X_test.shape[0] # Changing shape to a list for a singleton value if type(self._control_value) is not list: self._control_value = [self._control_value] if type(self._treatment_value) is not list: self._treatment_value = [self._treatment_value] T0_test = np.repeat([self._control_value], n_target_units, axis=0) T1_test = np.repeat([self._treatment_value], n_target_units, axis=0) est = self.estimator.effect(X_test, T0=T0_test, T1=T1_test) ate = np.mean(est) self.effect_intervals = None if self._confidence_intervals: self.effect_intervals = self.estimator.effect_interval( X_test, T0=T0_test, T1=T1_test, alpha=1 - self.confidence_level ) estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect(df[self._effect_modifier_names].values, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: return self.estimator.effect_inference(df[self._effect_modifier_names].values, *args, **kwargs)

import inspect from importlib import import_module from typing import Callable import numpy as np import pandas as pd from numpy.distutils.misc_util import is_sequence from dowhy.causal_estimator import CausalEstimate, CausalEstimator from dowhy.utils.api import parse_state class Econml(CausalEstimator): """Wrapper class for estimators from the EconML library. For a list of standard args and kwargs, see documentation for :class:`~dowhy.causal_estimator.CausalEstimator`. Supports additional parameters as listed below. For init and fit parameters of each estimator, refer to the EconML docs. """ def __init__(self, *args, econml_methodname, **kwargs): """ :param econml_methodname: Fully qualified name of econml estimator class. For example, 'econml.dml.DML' """ # Required to ensure that self.method_params contains all the # parameters to create an object of this class args_dict = {k: v for k, v in locals().items() if k not in type(self)._STD_INIT_ARGS} args_dict.update(kwargs) super().__init__(*args, **args_dict) self._econml_methodname = econml_methodname self.logger.info("INFO: Using EconML Estimator") self.identifier_method = self._target_estimand.identifier_method self._observed_common_causes_names = self._target_estimand.get_backdoor_variables().copy() # For metalearners only--issue a warning if w contains variables not in x (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): effect_modifier_names = [] if self._effect_modifier_names is not None: effect_modifier_names = self._effect_modifier_names.copy() w_diff_x = [w for w in self._observed_common_causes_names if w not in effect_modifier_names] if len(w_diff_x) > 0: self.logger.warn( "Concatenating common_causes and effect_modifiers and providing a single list of variables to metalearner estimator method, " + class_name + ". EconML metalearners accept a single X argument." ) effect_modifier_names.extend(w_diff_x) # Override the effect_modifiers set in CausalEstimator.__init__() # Also only update self._effect_modifiers, and create a copy of self._effect_modifier_names # the latter can be used by other estimator methods later self._effect_modifiers = self._data[effect_modifier_names] self._effect_modifiers = pd.get_dummies(self._effect_modifiers, drop_first=True) self._effect_modifier_names = effect_modifier_names self.logger.debug("Effect modifiers: " + ",".join(effect_modifier_names)) if self._observed_common_causes_names: self._observed_common_causes = self._data[self._observed_common_causes_names] self._observed_common_causes = pd.get_dummies(self._observed_common_causes, drop_first=True) else: self._observed_common_causes = None self.logger.debug("Back-door variables used:" + ",".join(self._observed_common_causes_names)) # Instrumental variables names, if present # choosing the instrumental variable to use if getattr(self, "iv_instrument_name", None) is None: self.estimating_instrument_names = self._target_estimand.instrumental_variables else: self.estimating_instrument_names = parse_state(self.iv_instrument_name) if self.estimating_instrument_names: self._estimating_instruments = self._data[self.estimating_instrument_names] self._estimating_instruments = pd.get_dummies(self._estimating_instruments, drop_first=True) else: self._estimating_instruments = None self.estimator = None self.symbolic_estimator = self.construct_symbolic_estimator(self._target_estimand) self.logger.info(self.symbolic_estimator) def _get_econml_class_object(self, module_method_name, *args, **kwargs): # from https://www.bnmetrics.com/blog/factory-pattern-in-python3-simple-version try: (module_name, _, class_name) = module_method_name.rpartition(".") estimator_module = import_module(module_name) estimator_class = getattr(estimator_module, class_name) except (AttributeError, AssertionError, ImportError): raise ImportError( "Error loading {}.{}. Double-check the method name and ensure that all econml dependencies are installed.".format( module_name, class_name ) ) return estimator_class def _estimate_effect(self): n_samples = self._treatment.shape[0] X = None # Effect modifiers W = None # common causes/ confounders Z = None # Instruments Y = self._outcome T = self._treatment if self._effect_modifiers is not None: X = self._effect_modifiers if self._observed_common_causes_names: W = self._observed_common_causes if self.estimating_instrument_names: Z = self._estimating_instruments named_data_args = {"Y": Y, "T": T, "X": X, "W": W, "Z": Z} if self.estimator is None: estimator_class = self._get_econml_class_object(self._econml_methodname) self.estimator = estimator_class(**self.method_params["init_params"]) # Calling the econml estimator's fit method estimator_argspec = inspect.getfullargspec(inspect.unwrap(self.estimator.fit)) # As of v0.9, econml has some kewyord only arguments estimator_named_args = estimator_argspec.args + estimator_argspec.kwonlyargs estimator_data_args = { arg: named_data_args[arg] for arg in named_data_args.keys() if arg in estimator_named_args } if self.method_params["fit_params"] is not False: self.estimator.fit(**estimator_data_args, **self.method_params["fit_params"]) X_test = X if X is not None: if type(self._target_units) is pd.DataFrame: X_test = self._target_units elif callable(self._target_units): filtered_rows = self._data.where(self._target_units) boolean_criterion = np.array(filtered_rows.notnull().iloc[:, 0]) X_test = X[boolean_criterion] # Changing shape to a list for a singleton value self._treatment_value = parse_state(self._treatment_value) est = self.effect(X_test) ate = np.mean(est, axis=0) # one value per treatment value if len(ate) == 1: ate = ate[0] if self._confidence_intervals: self.effect_intervals = self.effect_interval(X_test) else: self.effect_intervals = None estimate = CausalEstimate( estimate=ate, control_value=self._control_value, treatment_value=self._treatment_value, target_estimand=self._target_estimand, realized_estimand_expr=self.symbolic_estimator, cate_estimates=est, effect_intervals=self.effect_intervals, _estimator_object=self.estimator, ) return estimate def _estimate_confidence_intervals(self, confidence_level=None, method=None): """Returns None if the confidence interval has not been calculated.""" return self.effect_intervals def _do(self, x): raise NotImplementedError def construct_symbolic_estimator(self, estimand): expr = "b: " + ", ".join(estimand.outcome_variable) + "~" # TODO -- fix: we are actually conditioning on positive treatment (d=1) (module_name, _, class_name) = self._econml_methodname.rpartition(".") if module_name.endswith("metalearners"): var_list = estimand.treatment_variable + self._effect_modifier_names expr += "+".join(var_list) else: var_list = estimand.treatment_variable + self._observed_common_causes_names expr += "+".join(var_list) expr += " | " + ",".join(self._effect_modifier_names) return expr def shap_values(self, df: pd.DataFrame, *args, **kwargs): return self.estimator.shap_values(df[self._effect_modifier_names].values, *args, **kwargs) def apply_multitreatment(self, df: pd.DataFrame, fun: Callable, *args, **kwargs): ests = [] assert not isinstance(self._treatment_value, str) assert is_sequence(self._treatment_value) if df is None: filtered_df = None else: filtered_df = df[self._effect_modifier_names].values for tv in self._treatment_value: ests.append( fun( filtered_df, T0=self._control_value, T1=tv, *args, **kwargs, ) ) est = np.stack(ests, axis=1) return est def effect(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise estimated treatment effect, output shape n_units x n_treatment_values (not counting control) :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_fun, *args, **kwargs) def effect_interval(self, df: pd.DataFrame, *args, **kwargs) -> np.ndarray: """ Pointwise confidence intervals for the estimated treatment effect :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_interval_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_interval( filtered_df, T0=T0, T1=T1, alpha=1 - self.confidence_level, *args, **kwargs ) return self.apply_multitreatment(df, effect_interval_fun, *args, **kwargs) def effect_inference(self, df: pd.DataFrame, *args, **kwargs): """ Inference (uncertainty) results produced by the underlying EconML estimator :param df: Features of the units to evaluate :param args: passed through to the underlying estimator :param kwargs: passed through to the underlying estimator """ def effect_inference_fun(filtered_df, T0, T1, *args, **kwargs): return self.estimator.effect_inference(filtered_df, T0=T0, T1=T1, *args, **kwargs) return self.apply_multitreatment(df, effect_inference_fun, *args, **kwargs) def effect_tt(self, df: pd.DataFrame, *args, **kwargs): """ Effect of the actual treatment that was applied to each unit ("effect of Treatment on the Treated") :param df: Features of the units to evaluate :param args: passed through to estimator.effect() :param kwargs: passed through to estimator.effect() """ eff = self.effect(df, *args, **kwargs).reshape((len(df), len(self._treatment_value))) out = np.zeros(len(df)) treatment_value = parse_state(self._treatment_value) treatment_name = parse_state(self._treatment_name)[0] eff = np.reshape(eff, (len(df), len(treatment_value))) # For each unit, return the estimated effect of the treatment value # that was actually applied to the unit for c, col in enumerate(treatment_value): out[df[treatment_name] == col] = eff[df[treatment_name] == col, c] return pd.Series(data=out, index=df.index)

EgorKraevTransferwise

f83a276393f7f89e8c7991e5750c2f1095127e04

6cf8366c48b5f010952c14f615585a41cd37c3bf

Adding

EgorKraevTransferwise

py-why/dowhy

Adding autogluon as optional dependency to gcm module

This extends the auto model assignment by the 'BEST' parameter, which returns an autogluon model (i.e., an auto ML model).

2022-11-18 00:33:18+00:00

2022-11-23 21:05:13+00:00

poetry.lock

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bloebp

0a03cb10baddae6d6ca94d4d38fa074f5391b426

f83a276393f7f89e8c7991e5750c2f1095127e04

Please make sure you're on the latest poetry version. I believe latest uses underscores, not dashes. Let's try and keep noise in the lock as low as possible.

petergtz

py-why/dowhy

Adding autogluon as optional dependency to gcm module

This extends the auto model assignment by the 'BEST' parameter, which returns an autogluon model (i.e., an auto ML model).

2022-11-18 00:33:18+00:00

2022-11-23 21:05:13+00:00

poetry.lock

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bloebp

0a03cb10baddae6d6ca94d4d38fa074f5391b426

f83a276393f7f89e8c7991e5750c2f1095127e04

Sorted via Discord. Looks like the latest version of Poetry (1.2.2) actually does use dashes. Hopefully this will not be an issue anymore in the future.

petergtz

py-why/dowhy

Add convenience function to plot attribution scores

We're using function in so many places in notebooks, similar to the graph plot utility that I think it's worth providing this as a convenience function.

2022-11-15 22:35:03+00:00

2022-11-16 14:11:16+00:00

dowhy/gcm/util/plotting.py

import logging from typing import Any, Dict, List, Optional, Tuple import networkx as nx import pandas as pd from matplotlib import pyplot from networkx.drawing import nx_pydot _logger = logging.getLogger(__name__) def plot( causal_graph: nx.Graph, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, **kwargs, ) -> None: """Convenience function to plot causal graphs. This function uses different backends based on what's available on the system. The best result is achieved when using Graphviz as the backend. This requires both the Python pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. ``brew install graphviz`` or ``apt-get install graphviz``). When graphviz is not available, it will fall back to the networkx backend. :param causal_graph: The graph to be plotted :param causal_strengths: An optional dictionary with Edge -> float entries. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: A tuple to define the width and height (as a tuple) of the pyplot. This is used to parameter to modify pyplot's 'figure.figsize' parameter. If None is given, the current/default value is used. :param kwargs: Remaining parameters will be passed through to the backend verbatim. **Example usage**:: >>> plot(nx.DiGraph([('X', 'Y')])) # plots X -> Y >>> plot(nx.DiGraph([('X', 'Y')]), causal_strengths={('X', 'Y'): 0.43}) # annotates arrow with 0.43 """ try: from dowhy.gcm.util.pygraphviz import _plot_causal_graph_graphviz try: _plot_causal_graph_graphviz( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except Exception as error: _logger.info( "There was an error when trying to plot the graph via graphviz, falling back to networkx " "plotting. If graphviz is not installed, consider installing it for better looking plots. The" " error is:" + str(error) ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except ImportError: _logger.info( "Pygraphviz installation not found, falling back to networkx plotting. " "For better looking plots, consider installing pygraphviz. Note This requires both the Python " "pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. " "``brew install graphviz`` or ``apt-get install graphviz``)" ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) def plot_adjacency_matrix( adjacency_matrix: pd.DataFrame, is_directed: bool, filename: Optional[str] = None, display_plot: bool = True ) -> None: plot( nx.from_pandas_adjacency(adjacency_matrix, nx.DiGraph() if is_directed else nx.Graph()), display_plot=display_plot, filename=filename, ) def _plot_causal_graph_networkx( causal_graph: nx.Graph, pydot_layout_prog: Optional[str] = None, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, label_wrap_length: int = 3, figure_size: Optional[List[int]] = None, ) -> None: if "graph" not in causal_graph.graph: causal_graph.graph["graph"] = {"rankdir": "TD"} if pydot_layout_prog is not None: layout = nx_pydot.pydot_layout(causal_graph, prog=pydot_layout_prog) else: layout = nx.spring_layout(causal_graph) if causal_strengths is None: causal_strengths = {} max_strength = 0.0 for (source, target, strength) in causal_graph.edges(data="CAUSAL_STRENGTH", default=1): if (source, target) not in causal_strengths: causal_strengths[(source, target)] = strength max_strength = max(max_strength, abs(causal_strengths[(source, target)])) for edge in causal_graph.edges: if edge[0] == edge[1]: raise ValueError( "Node %s has a self-cycle, i.e. a node pointing to itself. Plotting self-cycles is " "currently only supported for plots using Graphviz! Consider installing the corresponding" "requirements." % edge[0] ) # Wrapping labels if they are too long labels = {} for node in causal_graph.nodes: node_name_splits = str(node).split(" ") for i in range(1, len(node_name_splits)): if len(node_name_splits[i - 1]) > label_wrap_length: node_name_splits[i] = "\n" + node_name_splits[i] else: node_name_splits[i] = " " + node_name_splits[i] labels[node] = "".join(node_name_splits) if figure_size is not None: org_fig_size = pyplot.rcParams["figure.figsize"] pyplot.rcParams["figure.figsize"] = figure_size figure = pyplot.figure() nx.draw( causal_graph, pos=layout, node_color="lightblue", linewidths=0.25, labels=labels, font_size=8, font_weight="bold", node_size=2000, width=[_calc_arrow_width(causal_strengths[(s, t)], max_strength) for (s, t) in causal_graph.edges()], ) if display_plot: pyplot.show() if figure_size is not None: pyplot.rcParams["figure.figsize"] = org_fig_size if filename is not None: figure.savefig(filename) def _calc_arrow_width(strength: float, max_strength: float): return 0.2 + 4.0 * float(abs(strength)) / float(max_strength)

import logging from typing import Any, Dict, List, Optional, Tuple import networkx as nx import numpy as np import pandas as pd from matplotlib import pyplot from networkx.drawing import nx_pydot _logger = logging.getLogger(__name__) def plot( causal_graph: nx.Graph, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, **kwargs, ) -> None: """Convenience function to plot causal graphs. This function uses different backends based on what's available on the system. The best result is achieved when using Graphviz as the backend. This requires both the Python pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. ``brew install graphviz`` or ``apt-get install graphviz``). When graphviz is not available, it will fall back to the networkx backend. :param causal_graph: The graph to be plotted :param causal_strengths: An optional dictionary with Edge -> float entries. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: A tuple to define the width and height (as a tuple) of the pyplot. This is used to parameter to modify pyplot's 'figure.figsize' parameter. If None is given, the current/default value is used. :param kwargs: Remaining parameters will be passed through to the backend verbatim. **Example usage**:: >>> plot(nx.DiGraph([('X', 'Y')])) # plots X -> Y >>> plot(nx.DiGraph([('X', 'Y')]), causal_strengths={('X', 'Y'): 0.43}) # annotates arrow with 0.43 """ try: from dowhy.gcm.util.pygraphviz import _plot_causal_graph_graphviz try: _plot_causal_graph_graphviz( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except Exception as error: _logger.info( "There was an error when trying to plot the graph via graphviz, falling back to networkx " "plotting. If graphviz is not installed, consider installing it for better looking plots. The" " error is:" + str(error) ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except ImportError: _logger.info( "Pygraphviz installation not found, falling back to networkx plotting. " "For better looking plots, consider installing pygraphviz. Note This requires both the Python " "pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. " "``brew install graphviz`` or ``apt-get install graphviz``)" ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) def plot_adjacency_matrix( adjacency_matrix: pd.DataFrame, is_directed: bool, filename: Optional[str] = None, display_plot: bool = True ) -> None: plot( nx.from_pandas_adjacency(adjacency_matrix, nx.DiGraph() if is_directed else nx.Graph()), display_plot=display_plot, filename=filename, ) def _plot_causal_graph_networkx( causal_graph: nx.Graph, pydot_layout_prog: Optional[str] = None, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, label_wrap_length: int = 3, figure_size: Optional[List[int]] = None, ) -> None: if "graph" not in causal_graph.graph: causal_graph.graph["graph"] = {"rankdir": "TD"} if pydot_layout_prog is not None: layout = nx_pydot.pydot_layout(causal_graph, prog=pydot_layout_prog) else: layout = nx.spring_layout(causal_graph) if causal_strengths is None: causal_strengths = {} max_strength = 0.0 for (source, target, strength) in causal_graph.edges(data="CAUSAL_STRENGTH", default=1): if (source, target) not in causal_strengths: causal_strengths[(source, target)] = strength max_strength = max(max_strength, abs(causal_strengths[(source, target)])) for edge in causal_graph.edges: if edge[0] == edge[1]: raise ValueError( "Node %s has a self-cycle, i.e. a node pointing to itself. Plotting self-cycles is " "currently only supported for plots using Graphviz! Consider installing the corresponding" "requirements." % edge[0] ) # Wrapping labels if they are too long labels = {} for node in causal_graph.nodes: node_name_splits = str(node).split(" ") for i in range(1, len(node_name_splits)): if len(node_name_splits[i - 1]) > label_wrap_length: node_name_splits[i] = "\n" + node_name_splits[i] else: node_name_splits[i] = " " + node_name_splits[i] labels[node] = "".join(node_name_splits) if figure_size is not None: org_fig_size = pyplot.rcParams["figure.figsize"] pyplot.rcParams["figure.figsize"] = figure_size figure = pyplot.figure() nx.draw( causal_graph, pos=layout, node_color="lightblue", linewidths=0.25, labels=labels, font_size=8, font_weight="bold", node_size=2000, width=[_calc_arrow_width(causal_strengths[(s, t)], max_strength) for (s, t) in causal_graph.edges()], ) if display_plot: pyplot.show() if figure_size is not None: pyplot.rcParams["figure.figsize"] = org_fig_size if filename is not None: figure.savefig(filename) def _calc_arrow_width(strength: float, max_strength: float): return 0.2 + 4.0 * float(abs(strength)) / float(max_strength) def bar_plot( values: Dict[str, float], uncertainties: Optional[Dict[str, Tuple[float, float]]] = None, ylabel: str = "", filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, bar_width: float = 0.8, xticks: List[str] = None, xticks_rotation: int = 90, ) -> None: """Convenience function to make a bar plot of the given values with uncertainty bars, if provided. Useful for all kinds of attribution results (including confidence intervals). :param values: A dictionary where the keys are the labels and the values are the values to be plotted. :param uncertainties: A dictionary of attributes to be added to the error bars. :param ylabel: The label for the y-axis. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: The size of the figure to be plotted. :param bar_width: The width of the bars. :param xticks: Explicitly specify the labels for the bars on the x-axis. :param xticks_rotation: Specify the rotation of the labels on the x-axis. """ if uncertainties is None: uncertainties = {node: [values[node], values[node]] for node in values} figure, ax = pyplot.subplots(figsize=figure_size) ci_plus = [uncertainties[node][1] - values[node] for node in values.keys()] ci_minus = [values[node] - uncertainties[node][0] for node in values.keys()] yerr = np.array([ci_minus, ci_plus]) yerr[abs(yerr) < 10**-7] = 0 pyplot.bar(values.keys(), values.values(), yerr=yerr, ecolor="#1E88E5", color="#ff0d57", width=bar_width) pyplot.ylabel(ylabel) pyplot.xticks(rotation=xticks_rotation) ax.spines["right"].set_visible(False) ax.spines["top"].set_visible(False) if xticks: pyplot.xticks(list(uncertainties.keys()), xticks) if display_plot: pyplot.show() if filename is not None: figure.savefig(filename)

petergtz

7568d9528b7108830821e8cc729c881523a58919

a067703ca430cb0a571ac31c9b90d21af8d0543b

It would be nice to have the xlabel as well. But not a must have.

kailashbuki

py-why/dowhy

Add convenience function to plot attribution scores

We're using function in so many places in notebooks, similar to the graph plot utility that I think it's worth providing this as a convenience function.

2022-11-15 22:35:03+00:00

2022-11-16 14:11:16+00:00

dowhy/gcm/util/plotting.py

import logging from typing import Any, Dict, List, Optional, Tuple import networkx as nx import pandas as pd from matplotlib import pyplot from networkx.drawing import nx_pydot _logger = logging.getLogger(__name__) def plot( causal_graph: nx.Graph, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, **kwargs, ) -> None: """Convenience function to plot causal graphs. This function uses different backends based on what's available on the system. The best result is achieved when using Graphviz as the backend. This requires both the Python pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. ``brew install graphviz`` or ``apt-get install graphviz``). When graphviz is not available, it will fall back to the networkx backend. :param causal_graph: The graph to be plotted :param causal_strengths: An optional dictionary with Edge -> float entries. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: A tuple to define the width and height (as a tuple) of the pyplot. This is used to parameter to modify pyplot's 'figure.figsize' parameter. If None is given, the current/default value is used. :param kwargs: Remaining parameters will be passed through to the backend verbatim. **Example usage**:: >>> plot(nx.DiGraph([('X', 'Y')])) # plots X -> Y >>> plot(nx.DiGraph([('X', 'Y')]), causal_strengths={('X', 'Y'): 0.43}) # annotates arrow with 0.43 """ try: from dowhy.gcm.util.pygraphviz import _plot_causal_graph_graphviz try: _plot_causal_graph_graphviz( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except Exception as error: _logger.info( "There was an error when trying to plot the graph via graphviz, falling back to networkx " "plotting. If graphviz is not installed, consider installing it for better looking plots. The" " error is:" + str(error) ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except ImportError: _logger.info( "Pygraphviz installation not found, falling back to networkx plotting. " "For better looking plots, consider installing pygraphviz. Note This requires both the Python " "pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. " "``brew install graphviz`` or ``apt-get install graphviz``)" ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) def plot_adjacency_matrix( adjacency_matrix: pd.DataFrame, is_directed: bool, filename: Optional[str] = None, display_plot: bool = True ) -> None: plot( nx.from_pandas_adjacency(adjacency_matrix, nx.DiGraph() if is_directed else nx.Graph()), display_plot=display_plot, filename=filename, ) def _plot_causal_graph_networkx( causal_graph: nx.Graph, pydot_layout_prog: Optional[str] = None, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, label_wrap_length: int = 3, figure_size: Optional[List[int]] = None, ) -> None: if "graph" not in causal_graph.graph: causal_graph.graph["graph"] = {"rankdir": "TD"} if pydot_layout_prog is not None: layout = nx_pydot.pydot_layout(causal_graph, prog=pydot_layout_prog) else: layout = nx.spring_layout(causal_graph) if causal_strengths is None: causal_strengths = {} max_strength = 0.0 for (source, target, strength) in causal_graph.edges(data="CAUSAL_STRENGTH", default=1): if (source, target) not in causal_strengths: causal_strengths[(source, target)] = strength max_strength = max(max_strength, abs(causal_strengths[(source, target)])) for edge in causal_graph.edges: if edge[0] == edge[1]: raise ValueError( "Node %s has a self-cycle, i.e. a node pointing to itself. Plotting self-cycles is " "currently only supported for plots using Graphviz! Consider installing the corresponding" "requirements." % edge[0] ) # Wrapping labels if they are too long labels = {} for node in causal_graph.nodes: node_name_splits = str(node).split(" ") for i in range(1, len(node_name_splits)): if len(node_name_splits[i - 1]) > label_wrap_length: node_name_splits[i] = "\n" + node_name_splits[i] else: node_name_splits[i] = " " + node_name_splits[i] labels[node] = "".join(node_name_splits) if figure_size is not None: org_fig_size = pyplot.rcParams["figure.figsize"] pyplot.rcParams["figure.figsize"] = figure_size figure = pyplot.figure() nx.draw( causal_graph, pos=layout, node_color="lightblue", linewidths=0.25, labels=labels, font_size=8, font_weight="bold", node_size=2000, width=[_calc_arrow_width(causal_strengths[(s, t)], max_strength) for (s, t) in causal_graph.edges()], ) if display_plot: pyplot.show() if figure_size is not None: pyplot.rcParams["figure.figsize"] = org_fig_size if filename is not None: figure.savefig(filename) def _calc_arrow_width(strength: float, max_strength: float): return 0.2 + 4.0 * float(abs(strength)) / float(max_strength)

import logging from typing import Any, Dict, List, Optional, Tuple import networkx as nx import numpy as np import pandas as pd from matplotlib import pyplot from networkx.drawing import nx_pydot _logger = logging.getLogger(__name__) def plot( causal_graph: nx.Graph, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, **kwargs, ) -> None: """Convenience function to plot causal graphs. This function uses different backends based on what's available on the system. The best result is achieved when using Graphviz as the backend. This requires both the Python pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. ``brew install graphviz`` or ``apt-get install graphviz``). When graphviz is not available, it will fall back to the networkx backend. :param causal_graph: The graph to be plotted :param causal_strengths: An optional dictionary with Edge -> float entries. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: A tuple to define the width and height (as a tuple) of the pyplot. This is used to parameter to modify pyplot's 'figure.figsize' parameter. If None is given, the current/default value is used. :param kwargs: Remaining parameters will be passed through to the backend verbatim. **Example usage**:: >>> plot(nx.DiGraph([('X', 'Y')])) # plots X -> Y >>> plot(nx.DiGraph([('X', 'Y')]), causal_strengths={('X', 'Y'): 0.43}) # annotates arrow with 0.43 """ try: from dowhy.gcm.util.pygraphviz import _plot_causal_graph_graphviz try: _plot_causal_graph_graphviz( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except Exception as error: _logger.info( "There was an error when trying to plot the graph via graphviz, falling back to networkx " "plotting. If graphviz is not installed, consider installing it for better looking plots. The" " error is:" + str(error) ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except ImportError: _logger.info( "Pygraphviz installation not found, falling back to networkx plotting. " "For better looking plots, consider installing pygraphviz. Note This requires both the Python " "pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. " "``brew install graphviz`` or ``apt-get install graphviz``)" ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) def plot_adjacency_matrix( adjacency_matrix: pd.DataFrame, is_directed: bool, filename: Optional[str] = None, display_plot: bool = True ) -> None: plot( nx.from_pandas_adjacency(adjacency_matrix, nx.DiGraph() if is_directed else nx.Graph()), display_plot=display_plot, filename=filename, ) def _plot_causal_graph_networkx( causal_graph: nx.Graph, pydot_layout_prog: Optional[str] = None, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, label_wrap_length: int = 3, figure_size: Optional[List[int]] = None, ) -> None: if "graph" not in causal_graph.graph: causal_graph.graph["graph"] = {"rankdir": "TD"} if pydot_layout_prog is not None: layout = nx_pydot.pydot_layout(causal_graph, prog=pydot_layout_prog) else: layout = nx.spring_layout(causal_graph) if causal_strengths is None: causal_strengths = {} max_strength = 0.0 for (source, target, strength) in causal_graph.edges(data="CAUSAL_STRENGTH", default=1): if (source, target) not in causal_strengths: causal_strengths[(source, target)] = strength max_strength = max(max_strength, abs(causal_strengths[(source, target)])) for edge in causal_graph.edges: if edge[0] == edge[1]: raise ValueError( "Node %s has a self-cycle, i.e. a node pointing to itself. Plotting self-cycles is " "currently only supported for plots using Graphviz! Consider installing the corresponding" "requirements." % edge[0] ) # Wrapping labels if they are too long labels = {} for node in causal_graph.nodes: node_name_splits = str(node).split(" ") for i in range(1, len(node_name_splits)): if len(node_name_splits[i - 1]) > label_wrap_length: node_name_splits[i] = "\n" + node_name_splits[i] else: node_name_splits[i] = " " + node_name_splits[i] labels[node] = "".join(node_name_splits) if figure_size is not None: org_fig_size = pyplot.rcParams["figure.figsize"] pyplot.rcParams["figure.figsize"] = figure_size figure = pyplot.figure() nx.draw( causal_graph, pos=layout, node_color="lightblue", linewidths=0.25, labels=labels, font_size=8, font_weight="bold", node_size=2000, width=[_calc_arrow_width(causal_strengths[(s, t)], max_strength) for (s, t) in causal_graph.edges()], ) if display_plot: pyplot.show() if figure_size is not None: pyplot.rcParams["figure.figsize"] = org_fig_size if filename is not None: figure.savefig(filename) def _calc_arrow_width(strength: float, max_strength: float): return 0.2 + 4.0 * float(abs(strength)) / float(max_strength) def bar_plot( values: Dict[str, float], uncertainties: Optional[Dict[str, Tuple[float, float]]] = None, ylabel: str = "", filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, bar_width: float = 0.8, xticks: List[str] = None, xticks_rotation: int = 90, ) -> None: """Convenience function to make a bar plot of the given values with uncertainty bars, if provided. Useful for all kinds of attribution results (including confidence intervals). :param values: A dictionary where the keys are the labels and the values are the values to be plotted. :param uncertainties: A dictionary of attributes to be added to the error bars. :param ylabel: The label for the y-axis. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: The size of the figure to be plotted. :param bar_width: The width of the bars. :param xticks: Explicitly specify the labels for the bars on the x-axis. :param xticks_rotation: Specify the rotation of the labels on the x-axis. """ if uncertainties is None: uncertainties = {node: [values[node], values[node]] for node in values} figure, ax = pyplot.subplots(figsize=figure_size) ci_plus = [uncertainties[node][1] - values[node] for node in values.keys()] ci_minus = [values[node] - uncertainties[node][0] for node in values.keys()] yerr = np.array([ci_minus, ci_plus]) yerr[abs(yerr) < 10**-7] = 0 pyplot.bar(values.keys(), values.values(), yerr=yerr, ecolor="#1E88E5", color="#ff0d57", width=bar_width) pyplot.ylabel(ylabel) pyplot.xticks(rotation=xticks_rotation) ax.spines["right"].set_visible(False) ax.spines["top"].set_visible(False) if xticks: pyplot.xticks(list(uncertainties.keys()), xticks) if display_plot: pyplot.show() if filename is not None: figure.savefig(filename)

petergtz

7568d9528b7108830821e8cc729c881523a58919

a067703ca430cb0a571ac31c9b90d21af8d0543b

Optionally: Can add something like `**kwargs_bar_plot`, which are passed into the `pyplot.bar` call.

bloebp

py-why/dowhy

Add convenience function to plot attribution scores

We're using function in so many places in notebooks, similar to the graph plot utility that I think it's worth providing this as a convenience function.

2022-11-15 22:35:03+00:00

2022-11-16 14:11:16+00:00

dowhy/gcm/util/plotting.py

import logging from typing import Any, Dict, List, Optional, Tuple import networkx as nx import pandas as pd from matplotlib import pyplot from networkx.drawing import nx_pydot _logger = logging.getLogger(__name__) def plot( causal_graph: nx.Graph, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, **kwargs, ) -> None: """Convenience function to plot causal graphs. This function uses different backends based on what's available on the system. The best result is achieved when using Graphviz as the backend. This requires both the Python pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. ``brew install graphviz`` or ``apt-get install graphviz``). When graphviz is not available, it will fall back to the networkx backend. :param causal_graph: The graph to be plotted :param causal_strengths: An optional dictionary with Edge -> float entries. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: A tuple to define the width and height (as a tuple) of the pyplot. This is used to parameter to modify pyplot's 'figure.figsize' parameter. If None is given, the current/default value is used. :param kwargs: Remaining parameters will be passed through to the backend verbatim. **Example usage**:: >>> plot(nx.DiGraph([('X', 'Y')])) # plots X -> Y >>> plot(nx.DiGraph([('X', 'Y')]), causal_strengths={('X', 'Y'): 0.43}) # annotates arrow with 0.43 """ try: from dowhy.gcm.util.pygraphviz import _plot_causal_graph_graphviz try: _plot_causal_graph_graphviz( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except Exception as error: _logger.info( "There was an error when trying to plot the graph via graphviz, falling back to networkx " "plotting. If graphviz is not installed, consider installing it for better looking plots. The" " error is:" + str(error) ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except ImportError: _logger.info( "Pygraphviz installation not found, falling back to networkx plotting. " "For better looking plots, consider installing pygraphviz. Note This requires both the Python " "pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. " "``brew install graphviz`` or ``apt-get install graphviz``)" ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) def plot_adjacency_matrix( adjacency_matrix: pd.DataFrame, is_directed: bool, filename: Optional[str] = None, display_plot: bool = True ) -> None: plot( nx.from_pandas_adjacency(adjacency_matrix, nx.DiGraph() if is_directed else nx.Graph()), display_plot=display_plot, filename=filename, ) def _plot_causal_graph_networkx( causal_graph: nx.Graph, pydot_layout_prog: Optional[str] = None, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, label_wrap_length: int = 3, figure_size: Optional[List[int]] = None, ) -> None: if "graph" not in causal_graph.graph: causal_graph.graph["graph"] = {"rankdir": "TD"} if pydot_layout_prog is not None: layout = nx_pydot.pydot_layout(causal_graph, prog=pydot_layout_prog) else: layout = nx.spring_layout(causal_graph) if causal_strengths is None: causal_strengths = {} max_strength = 0.0 for (source, target, strength) in causal_graph.edges(data="CAUSAL_STRENGTH", default=1): if (source, target) not in causal_strengths: causal_strengths[(source, target)] = strength max_strength = max(max_strength, abs(causal_strengths[(source, target)])) for edge in causal_graph.edges: if edge[0] == edge[1]: raise ValueError( "Node %s has a self-cycle, i.e. a node pointing to itself. Plotting self-cycles is " "currently only supported for plots using Graphviz! Consider installing the corresponding" "requirements." % edge[0] ) # Wrapping labels if they are too long labels = {} for node in causal_graph.nodes: node_name_splits = str(node).split(" ") for i in range(1, len(node_name_splits)): if len(node_name_splits[i - 1]) > label_wrap_length: node_name_splits[i] = "\n" + node_name_splits[i] else: node_name_splits[i] = " " + node_name_splits[i] labels[node] = "".join(node_name_splits) if figure_size is not None: org_fig_size = pyplot.rcParams["figure.figsize"] pyplot.rcParams["figure.figsize"] = figure_size figure = pyplot.figure() nx.draw( causal_graph, pos=layout, node_color="lightblue", linewidths=0.25, labels=labels, font_size=8, font_weight="bold", node_size=2000, width=[_calc_arrow_width(causal_strengths[(s, t)], max_strength) for (s, t) in causal_graph.edges()], ) if display_plot: pyplot.show() if figure_size is not None: pyplot.rcParams["figure.figsize"] = org_fig_size if filename is not None: figure.savefig(filename) def _calc_arrow_width(strength: float, max_strength: float): return 0.2 + 4.0 * float(abs(strength)) / float(max_strength)

import logging from typing import Any, Dict, List, Optional, Tuple import networkx as nx import numpy as np import pandas as pd from matplotlib import pyplot from networkx.drawing import nx_pydot _logger = logging.getLogger(__name__) def plot( causal_graph: nx.Graph, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, **kwargs, ) -> None: """Convenience function to plot causal graphs. This function uses different backends based on what's available on the system. The best result is achieved when using Graphviz as the backend. This requires both the Python pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. ``brew install graphviz`` or ``apt-get install graphviz``). When graphviz is not available, it will fall back to the networkx backend. :param causal_graph: The graph to be plotted :param causal_strengths: An optional dictionary with Edge -> float entries. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: A tuple to define the width and height (as a tuple) of the pyplot. This is used to parameter to modify pyplot's 'figure.figsize' parameter. If None is given, the current/default value is used. :param kwargs: Remaining parameters will be passed through to the backend verbatim. **Example usage**:: >>> plot(nx.DiGraph([('X', 'Y')])) # plots X -> Y >>> plot(nx.DiGraph([('X', 'Y')]), causal_strengths={('X', 'Y'): 0.43}) # annotates arrow with 0.43 """ try: from dowhy.gcm.util.pygraphviz import _plot_causal_graph_graphviz try: _plot_causal_graph_graphviz( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except Exception as error: _logger.info( "There was an error when trying to plot the graph via graphviz, falling back to networkx " "plotting. If graphviz is not installed, consider installing it for better looking plots. The" " error is:" + str(error) ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except ImportError: _logger.info( "Pygraphviz installation not found, falling back to networkx plotting. " "For better looking plots, consider installing pygraphviz. Note This requires both the Python " "pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. " "``brew install graphviz`` or ``apt-get install graphviz``)" ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) def plot_adjacency_matrix( adjacency_matrix: pd.DataFrame, is_directed: bool, filename: Optional[str] = None, display_plot: bool = True ) -> None: plot( nx.from_pandas_adjacency(adjacency_matrix, nx.DiGraph() if is_directed else nx.Graph()), display_plot=display_plot, filename=filename, ) def _plot_causal_graph_networkx( causal_graph: nx.Graph, pydot_layout_prog: Optional[str] = None, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, label_wrap_length: int = 3, figure_size: Optional[List[int]] = None, ) -> None: if "graph" not in causal_graph.graph: causal_graph.graph["graph"] = {"rankdir": "TD"} if pydot_layout_prog is not None: layout = nx_pydot.pydot_layout(causal_graph, prog=pydot_layout_prog) else: layout = nx.spring_layout(causal_graph) if causal_strengths is None: causal_strengths = {} max_strength = 0.0 for (source, target, strength) in causal_graph.edges(data="CAUSAL_STRENGTH", default=1): if (source, target) not in causal_strengths: causal_strengths[(source, target)] = strength max_strength = max(max_strength, abs(causal_strengths[(source, target)])) for edge in causal_graph.edges: if edge[0] == edge[1]: raise ValueError( "Node %s has a self-cycle, i.e. a node pointing to itself. Plotting self-cycles is " "currently only supported for plots using Graphviz! Consider installing the corresponding" "requirements." % edge[0] ) # Wrapping labels if they are too long labels = {} for node in causal_graph.nodes: node_name_splits = str(node).split(" ") for i in range(1, len(node_name_splits)): if len(node_name_splits[i - 1]) > label_wrap_length: node_name_splits[i] = "\n" + node_name_splits[i] else: node_name_splits[i] = " " + node_name_splits[i] labels[node] = "".join(node_name_splits) if figure_size is not None: org_fig_size = pyplot.rcParams["figure.figsize"] pyplot.rcParams["figure.figsize"] = figure_size figure = pyplot.figure() nx.draw( causal_graph, pos=layout, node_color="lightblue", linewidths=0.25, labels=labels, font_size=8, font_weight="bold", node_size=2000, width=[_calc_arrow_width(causal_strengths[(s, t)], max_strength) for (s, t) in causal_graph.edges()], ) if display_plot: pyplot.show() if figure_size is not None: pyplot.rcParams["figure.figsize"] = org_fig_size if filename is not None: figure.savefig(filename) def _calc_arrow_width(strength: float, max_strength: float): return 0.2 + 4.0 * float(abs(strength)) / float(max_strength) def bar_plot( values: Dict[str, float], uncertainties: Optional[Dict[str, Tuple[float, float]]] = None, ylabel: str = "", filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, bar_width: float = 0.8, xticks: List[str] = None, xticks_rotation: int = 90, ) -> None: """Convenience function to make a bar plot of the given values with uncertainty bars, if provided. Useful for all kinds of attribution results (including confidence intervals). :param values: A dictionary where the keys are the labels and the values are the values to be plotted. :param uncertainties: A dictionary of attributes to be added to the error bars. :param ylabel: The label for the y-axis. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: The size of the figure to be plotted. :param bar_width: The width of the bars. :param xticks: Explicitly specify the labels for the bars on the x-axis. :param xticks_rotation: Specify the rotation of the labels on the x-axis. """ if uncertainties is None: uncertainties = {node: [values[node], values[node]] for node in values} figure, ax = pyplot.subplots(figsize=figure_size) ci_plus = [uncertainties[node][1] - values[node] for node in values.keys()] ci_minus = [values[node] - uncertainties[node][0] for node in values.keys()] yerr = np.array([ci_minus, ci_plus]) yerr[abs(yerr) < 10**-7] = 0 pyplot.bar(values.keys(), values.values(), yerr=yerr, ecolor="#1E88E5", color="#ff0d57", width=bar_width) pyplot.ylabel(ylabel) pyplot.xticks(rotation=xticks_rotation) ax.spines["right"].set_visible(False) ax.spines["top"].set_visible(False) if xticks: pyplot.xticks(list(uncertainties.keys()), xticks) if display_plot: pyplot.show() if filename is not None: figure.savefig(filename)

petergtz

7568d9528b7108830821e8cc729c881523a58919

a067703ca430cb0a571ac31c9b90d21af8d0543b

I'll add them in a follow-up PR.

petergtz

py-why/dowhy

Add convenience function to plot attribution scores

We're using function in so many places in notebooks, similar to the graph plot utility that I think it's worth providing this as a convenience function.

2022-11-15 22:35:03+00:00

2022-11-16 14:11:16+00:00

dowhy/gcm/util/plotting.py

import logging from typing import Any, Dict, List, Optional, Tuple import networkx as nx import pandas as pd from matplotlib import pyplot from networkx.drawing import nx_pydot _logger = logging.getLogger(__name__) def plot( causal_graph: nx.Graph, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, **kwargs, ) -> None: """Convenience function to plot causal graphs. This function uses different backends based on what's available on the system. The best result is achieved when using Graphviz as the backend. This requires both the Python pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. ``brew install graphviz`` or ``apt-get install graphviz``). When graphviz is not available, it will fall back to the networkx backend. :param causal_graph: The graph to be plotted :param causal_strengths: An optional dictionary with Edge -> float entries. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: A tuple to define the width and height (as a tuple) of the pyplot. This is used to parameter to modify pyplot's 'figure.figsize' parameter. If None is given, the current/default value is used. :param kwargs: Remaining parameters will be passed through to the backend verbatim. **Example usage**:: >>> plot(nx.DiGraph([('X', 'Y')])) # plots X -> Y >>> plot(nx.DiGraph([('X', 'Y')]), causal_strengths={('X', 'Y'): 0.43}) # annotates arrow with 0.43 """ try: from dowhy.gcm.util.pygraphviz import _plot_causal_graph_graphviz try: _plot_causal_graph_graphviz( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except Exception as error: _logger.info( "There was an error when trying to plot the graph via graphviz, falling back to networkx " "plotting. If graphviz is not installed, consider installing it for better looking plots. The" " error is:" + str(error) ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except ImportError: _logger.info( "Pygraphviz installation not found, falling back to networkx plotting. " "For better looking plots, consider installing pygraphviz. Note This requires both the Python " "pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. " "``brew install graphviz`` or ``apt-get install graphviz``)" ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) def plot_adjacency_matrix( adjacency_matrix: pd.DataFrame, is_directed: bool, filename: Optional[str] = None, display_plot: bool = True ) -> None: plot( nx.from_pandas_adjacency(adjacency_matrix, nx.DiGraph() if is_directed else nx.Graph()), display_plot=display_plot, filename=filename, ) def _plot_causal_graph_networkx( causal_graph: nx.Graph, pydot_layout_prog: Optional[str] = None, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, label_wrap_length: int = 3, figure_size: Optional[List[int]] = None, ) -> None: if "graph" not in causal_graph.graph: causal_graph.graph["graph"] = {"rankdir": "TD"} if pydot_layout_prog is not None: layout = nx_pydot.pydot_layout(causal_graph, prog=pydot_layout_prog) else: layout = nx.spring_layout(causal_graph) if causal_strengths is None: causal_strengths = {} max_strength = 0.0 for (source, target, strength) in causal_graph.edges(data="CAUSAL_STRENGTH", default=1): if (source, target) not in causal_strengths: causal_strengths[(source, target)] = strength max_strength = max(max_strength, abs(causal_strengths[(source, target)])) for edge in causal_graph.edges: if edge[0] == edge[1]: raise ValueError( "Node %s has a self-cycle, i.e. a node pointing to itself. Plotting self-cycles is " "currently only supported for plots using Graphviz! Consider installing the corresponding" "requirements." % edge[0] ) # Wrapping labels if they are too long labels = {} for node in causal_graph.nodes: node_name_splits = str(node).split(" ") for i in range(1, len(node_name_splits)): if len(node_name_splits[i - 1]) > label_wrap_length: node_name_splits[i] = "\n" + node_name_splits[i] else: node_name_splits[i] = " " + node_name_splits[i] labels[node] = "".join(node_name_splits) if figure_size is not None: org_fig_size = pyplot.rcParams["figure.figsize"] pyplot.rcParams["figure.figsize"] = figure_size figure = pyplot.figure() nx.draw( causal_graph, pos=layout, node_color="lightblue", linewidths=0.25, labels=labels, font_size=8, font_weight="bold", node_size=2000, width=[_calc_arrow_width(causal_strengths[(s, t)], max_strength) for (s, t) in causal_graph.edges()], ) if display_plot: pyplot.show() if figure_size is not None: pyplot.rcParams["figure.figsize"] = org_fig_size if filename is not None: figure.savefig(filename) def _calc_arrow_width(strength: float, max_strength: float): return 0.2 + 4.0 * float(abs(strength)) / float(max_strength)

import logging from typing import Any, Dict, List, Optional, Tuple import networkx as nx import numpy as np import pandas as pd from matplotlib import pyplot from networkx.drawing import nx_pydot _logger = logging.getLogger(__name__) def plot( causal_graph: nx.Graph, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, **kwargs, ) -> None: """Convenience function to plot causal graphs. This function uses different backends based on what's available on the system. The best result is achieved when using Graphviz as the backend. This requires both the Python pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. ``brew install graphviz`` or ``apt-get install graphviz``). When graphviz is not available, it will fall back to the networkx backend. :param causal_graph: The graph to be plotted :param causal_strengths: An optional dictionary with Edge -> float entries. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: A tuple to define the width and height (as a tuple) of the pyplot. This is used to parameter to modify pyplot's 'figure.figsize' parameter. If None is given, the current/default value is used. :param kwargs: Remaining parameters will be passed through to the backend verbatim. **Example usage**:: >>> plot(nx.DiGraph([('X', 'Y')])) # plots X -> Y >>> plot(nx.DiGraph([('X', 'Y')]), causal_strengths={('X', 'Y'): 0.43}) # annotates arrow with 0.43 """ try: from dowhy.gcm.util.pygraphviz import _plot_causal_graph_graphviz try: _plot_causal_graph_graphviz( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except Exception as error: _logger.info( "There was an error when trying to plot the graph via graphviz, falling back to networkx " "plotting. If graphviz is not installed, consider installing it for better looking plots. The" " error is:" + str(error) ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) except ImportError: _logger.info( "Pygraphviz installation not found, falling back to networkx plotting. " "For better looking plots, consider installing pygraphviz. Note This requires both the Python " "pygraphviz package (``pip install pygraphviz``) and the shared system library (e.g. " "``brew install graphviz`` or ``apt-get install graphviz``)" ) _plot_causal_graph_networkx( causal_graph, causal_strengths=causal_strengths, filename=filename, display_plot=display_plot, figure_size=figure_size, **kwargs, ) def plot_adjacency_matrix( adjacency_matrix: pd.DataFrame, is_directed: bool, filename: Optional[str] = None, display_plot: bool = True ) -> None: plot( nx.from_pandas_adjacency(adjacency_matrix, nx.DiGraph() if is_directed else nx.Graph()), display_plot=display_plot, filename=filename, ) def _plot_causal_graph_networkx( causal_graph: nx.Graph, pydot_layout_prog: Optional[str] = None, causal_strengths: Optional[Dict[Tuple[Any, Any], float]] = None, filename: Optional[str] = None, display_plot: bool = True, label_wrap_length: int = 3, figure_size: Optional[List[int]] = None, ) -> None: if "graph" not in causal_graph.graph: causal_graph.graph["graph"] = {"rankdir": "TD"} if pydot_layout_prog is not None: layout = nx_pydot.pydot_layout(causal_graph, prog=pydot_layout_prog) else: layout = nx.spring_layout(causal_graph) if causal_strengths is None: causal_strengths = {} max_strength = 0.0 for (source, target, strength) in causal_graph.edges(data="CAUSAL_STRENGTH", default=1): if (source, target) not in causal_strengths: causal_strengths[(source, target)] = strength max_strength = max(max_strength, abs(causal_strengths[(source, target)])) for edge in causal_graph.edges: if edge[0] == edge[1]: raise ValueError( "Node %s has a self-cycle, i.e. a node pointing to itself. Plotting self-cycles is " "currently only supported for plots using Graphviz! Consider installing the corresponding" "requirements." % edge[0] ) # Wrapping labels if they are too long labels = {} for node in causal_graph.nodes: node_name_splits = str(node).split(" ") for i in range(1, len(node_name_splits)): if len(node_name_splits[i - 1]) > label_wrap_length: node_name_splits[i] = "\n" + node_name_splits[i] else: node_name_splits[i] = " " + node_name_splits[i] labels[node] = "".join(node_name_splits) if figure_size is not None: org_fig_size = pyplot.rcParams["figure.figsize"] pyplot.rcParams["figure.figsize"] = figure_size figure = pyplot.figure() nx.draw( causal_graph, pos=layout, node_color="lightblue", linewidths=0.25, labels=labels, font_size=8, font_weight="bold", node_size=2000, width=[_calc_arrow_width(causal_strengths[(s, t)], max_strength) for (s, t) in causal_graph.edges()], ) if display_plot: pyplot.show() if figure_size is not None: pyplot.rcParams["figure.figsize"] = org_fig_size if filename is not None: figure.savefig(filename) def _calc_arrow_width(strength: float, max_strength: float): return 0.2 + 4.0 * float(abs(strength)) / float(max_strength) def bar_plot( values: Dict[str, float], uncertainties: Optional[Dict[str, Tuple[float, float]]] = None, ylabel: str = "", filename: Optional[str] = None, display_plot: bool = True, figure_size: Optional[List[int]] = None, bar_width: float = 0.8, xticks: List[str] = None, xticks_rotation: int = 90, ) -> None: """Convenience function to make a bar plot of the given values with uncertainty bars, if provided. Useful for all kinds of attribution results (including confidence intervals). :param values: A dictionary where the keys are the labels and the values are the values to be plotted. :param uncertainties: A dictionary of attributes to be added to the error bars. :param ylabel: The label for the y-axis. :param filename: An optional filename if the output should be plotted into a file. :param display_plot: Optionally specify if the plot should be displayed or not (default to True). :param figure_size: The size of the figure to be plotted. :param bar_width: The width of the bars. :param xticks: Explicitly specify the labels for the bars on the x-axis. :param xticks_rotation: Specify the rotation of the labels on the x-axis. """ if uncertainties is None: uncertainties = {node: [values[node], values[node]] for node in values} figure, ax = pyplot.subplots(figsize=figure_size) ci_plus = [uncertainties[node][1] - values[node] for node in values.keys()] ci_minus = [values[node] - uncertainties[node][0] for node in values.keys()] yerr = np.array([ci_minus, ci_plus]) yerr[abs(yerr) < 10**-7] = 0 pyplot.bar(values.keys(), values.values(), yerr=yerr, ecolor="#1E88E5", color="#ff0d57", width=bar_width) pyplot.ylabel(ylabel) pyplot.xticks(rotation=xticks_rotation) ax.spines["right"].set_visible(False) ax.spines["top"].set_visible(False) if xticks: pyplot.xticks(list(uncertainties.keys()), xticks) if display_plot: pyplot.show() if filename is not None: figure.savefig(filename)

petergtz

7568d9528b7108830821e8cc729c881523a58919

a067703ca430cb0a571ac31c9b90d21af8d0543b

Fair. I'd still post-pone this into a separate PR.

petergtz

py-why/dowhy

Add APIs for attributing unit change without a mechanism change

- Added two new APIs for attributing unit-level output changes when the mechanism does not change. Signed-off-by: Kailash <111277+kailashbuki@users.noreply.github.com>

2022-11-14 09:40:52+00:00

2022-11-14 21:51:34+00:00

dowhy/gcm/unit_change.py

"""This module provides the APIs for attributing the change in the output value of a deterministic mechanism for a statistical unit. """ from abc import abstractmethod from typing import List, Optional import numpy as np import pandas as pd from sklearn.linear_model._base import LinearModel from sklearn.utils.validation import check_is_fitted from dowhy.gcm.fcms import PredictionModel from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.shapley import ShapleyConfig, estimate_shapley_values class LinearPredictionModel: @property @abstractmethod def coefficients(self) -> np.ndarray: pass class SklearnLinearRegressionModel(SklearnRegressionModel, LinearPredictionModel): def __init__(self, sklearn_mdl: LinearModel) -> None: super(SklearnLinearRegressionModel, self).__init__(sklearn_mdl) @property def coefficients(self) -> np.ndarray: check_is_fitted(self.sklearn_model) return self.sklearn_model.coef_ def unit_change_nonlinear( background_mechanism: PredictionModel, background_df: pd.DataFrame, foreground_mechanism: PredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a non-linear deterministic mechanism. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_mechanism: The background mechanism. :param background_df: The background data. :param foreground_mechanism: The foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(binary_vector: List[int]) -> np.ndarray: """The last cell in the binary vector represents the player 'mechanism'.""" background_column_names = [input_column_names[i] for i, val in enumerate(binary_vector[:-1]) if val == 0] foreground_column_names = [input_column_names[i] for i, val in enumerate(binary_vector[:-1]) if val == 1] df = pd.concat([background_df[background_column_names], foreground_df[foreground_column_names]], axis=1) mechanism = foreground_mechanism if binary_vector[-1] else background_mechanism return mechanism.predict(df[input_column_names].values).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names) + 1, shapley_config) root_causes = input_column_names + ["f"] return pd.DataFrame(contributions, columns=root_causes) def unit_change_linear( background_mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_mechanism: LinearPredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a linear deterministic mechanism. :param background_mechanism: The linear background mechanism. :param background_df: The background data. :param foreground_mechanism: The linear foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) coeffs_total = background_mechanism.coefficients + foreground_mechanism.coefficients # p x 1 coeffs_diff = foreground_mechanism.coefficients - background_mechanism.coefficients # p x 1 input_total = foreground_df[input_column_names].to_numpy() + background_df[input_column_names].to_numpy() # n x p input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = 0.5 * np.einsum("ij,ki->ki", coeffs_total.reshape(-1, 1), input_diff) contribution_mechanism = 0.5 * np.einsum("ij,ki->k", coeffs_diff.reshape(-1, 1), input_total) contribution_df = pd.DataFrame(contribution_input, columns=input_column_names) contribution_df["f"] = contribution_mechanism # TODO: Handle the case where 'f' is an input column name return contribution_df def _check_if_input_columns_exist( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str] ) -> None: if not len(set(background_df.columns).intersection(input_column_names)) == len(input_column_names) or not len( set(foreground_df.columns).intersection(input_column_names) ) == len(input_column_names): raise ValueError("Input column names not found in either the background or the foreground data.")

"""This module provides the APIs for attributing the change in the output value of a deterministic mechanism for a statistical unit. """ from abc import abstractmethod from typing import List, Optional import numpy as np import pandas as pd from sklearn.linear_model._base import LinearModel from sklearn.utils.validation import check_is_fitted from dowhy.gcm.fcms import PredictionModel from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.shapley import ShapleyConfig, estimate_shapley_values class LinearPredictionModel: @property @abstractmethod def coefficients(self) -> np.ndarray: pass class SklearnLinearRegressionModel(SklearnRegressionModel, LinearPredictionModel): def __init__(self, sklearn_mdl: LinearModel) -> None: super(SklearnLinearRegressionModel, self).__init__(sklearn_mdl) @property def coefficients(self) -> np.ndarray: check_is_fitted(self.sklearn_model) return self.sklearn_model.coef_ def unit_change( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], background_mechanism: PredictionModel, foreground_mechanism: Optional[PredictionModel] = None, shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ This function attributes the change in the output value of a deterministic mechanism for a statistical unit to each input and optionally for the mechanism if `foreground_mechanism` is provided. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_df: The background dataset. :param foreground_df: The foreground dataset. :param input_column_names: The names of the input columns. :param background_mechanism: The background mechanism. If the mechanism does not change, then this mechanism is used for attribution. :param foreground_mechanism: The foreground mechanism. If provided, the method also attributes the output change to the change in the mechanism. :param shapley_config: The configuration for calculating Shapley values. :return: A dataframe containing the contributions of each input and optionally the mechanism to the change in the output values of the deterministic mechanism(s) for given inputs. """ if foreground_mechanism: if isinstance(background_mechanism, LinearPredictionModel): return unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, input_column_names ) else: return unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, input_column_names, shapley_config, ) if isinstance(background_mechanism, LinearPredictionModel): return unit_change_linear_input_only(background_mechanism, background_df, foreground_df, input_column_names) else: return unit_change_nonlinear_input_only( background_mechanism, background_df, foreground_df, input_column_names, shapley_config ) def unit_change_nonlinear( background_mechanism: PredictionModel, background_df: pd.DataFrame, foreground_mechanism: PredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a non-linear deterministic mechanism. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_mechanism: The background mechanism. :param background_df: The background data. :param foreground_mechanism: The foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(player_indicator: List[int]) -> np.ndarray: """The last cell in the binary vector represents the player 'mechanism'.""" input_arrays = [] for i, is_player_active in enumerate(player_indicator[:-1]): selected_df = foreground_df if is_player_active else background_df input_arrays.append(selected_df[input_column_names[i]].to_numpy()) mechanism = foreground_mechanism if player_indicator[-1] else background_mechanism return mechanism.predict(np.column_stack(input_arrays)).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names) + 1, shapley_config) root_causes = input_column_names + ["f"] return pd.DataFrame(contributions, columns=root_causes) def unit_change_linear( background_mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_mechanism: LinearPredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a linear deterministic mechanism. :param background_mechanism: The linear background mechanism. :param background_df: The background data. :param foreground_mechanism: The linear foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) coeffs_total = background_mechanism.coefficients + foreground_mechanism.coefficients # p x 1 coeffs_diff = foreground_mechanism.coefficients - background_mechanism.coefficients # p x 1 input_total = foreground_df[input_column_names].to_numpy() + background_df[input_column_names].to_numpy() # n x p input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = 0.5 * np.einsum("ij,ki->ki", coeffs_total.reshape(-1, 1), input_diff) contribution_mechanism = 0.5 * np.einsum("ij,ki->k", coeffs_diff.reshape(-1, 1), input_total) contribution_df = pd.DataFrame(contribution_input, columns=input_column_names) contribution_df["f"] = contribution_mechanism # TODO: Handle the case where 'f' is an input column name return contribution_df def unit_change_nonlinear_input_only( mechanism: PredictionModel, background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of each input to the change in the output values of a non-linear deterministic mechanism. The technical method is a modification of the attribution method described in the following research paper, without mechanism as a player: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param mechanism: The mechanism. :param background_df: The background data. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(player_indicator: List[int]) -> np.ndarray: input_arrays = [] for i, is_player_active in enumerate(player_indicator): selected_df = foreground_df if is_player_active else background_df input_arrays.append(selected_df[input_column_names[i]].to_numpy()) return mechanism.predict(np.column_stack(input_arrays)).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names), shapley_config) return pd.DataFrame(contributions, columns=input_column_names) def unit_change_linear_input_only( mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of each input to the change in the output values of a linear deterministic mechanism. :param mechanism: The linear mechanism. :param background_df: The background data. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = np.einsum("ij,ki->ki", mechanism.coefficients.reshape(-1, 1), input_diff) return pd.DataFrame(contribution_input, columns=input_column_names) def _check_if_input_columns_exist( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str] ) -> None: if not len(set(background_df.columns).intersection(input_column_names)) == len(input_column_names) or not len( set(foreground_df.columns).intersection(input_column_names) ) == len(input_column_names): raise ValueError("Input column names not found in either the background or the foreground data.")

kailashbuki

675cbc444cc422b007ba72fdf3303b328b123c48

ac047066326d0de3646f8461c0c5c4dd9826287c

What about using ```if isinstance(mechanism, LinearPredictionModel)``` and then have only one method ```unit_change_input_only```? Same applies to the existing method. To further simplify it (i.e., avoid having multiple different methods), you could also consider adding a parameter ```analyze_inputs_only``` to the other existing method. Then, there would only be one API to call that can be configured and only requires one additional parameter. Or are these two approaches fundamentally different?

bloebp

py-why/dowhy

Add APIs for attributing unit change without a mechanism change

- Added two new APIs for attributing unit-level output changes when the mechanism does not change. Signed-off-by: Kailash <111277+kailashbuki@users.noreply.github.com>

2022-11-14 09:40:52+00:00

2022-11-14 21:51:34+00:00

dowhy/gcm/unit_change.py

"""This module provides the APIs for attributing the change in the output value of a deterministic mechanism for a statistical unit. """ from abc import abstractmethod from typing import List, Optional import numpy as np import pandas as pd from sklearn.linear_model._base import LinearModel from sklearn.utils.validation import check_is_fitted from dowhy.gcm.fcms import PredictionModel from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.shapley import ShapleyConfig, estimate_shapley_values class LinearPredictionModel: @property @abstractmethod def coefficients(self) -> np.ndarray: pass class SklearnLinearRegressionModel(SklearnRegressionModel, LinearPredictionModel): def __init__(self, sklearn_mdl: LinearModel) -> None: super(SklearnLinearRegressionModel, self).__init__(sklearn_mdl) @property def coefficients(self) -> np.ndarray: check_is_fitted(self.sklearn_model) return self.sklearn_model.coef_ def unit_change_nonlinear( background_mechanism: PredictionModel, background_df: pd.DataFrame, foreground_mechanism: PredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a non-linear deterministic mechanism. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_mechanism: The background mechanism. :param background_df: The background data. :param foreground_mechanism: The foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(binary_vector: List[int]) -> np.ndarray: """The last cell in the binary vector represents the player 'mechanism'.""" background_column_names = [input_column_names[i] for i, val in enumerate(binary_vector[:-1]) if val == 0] foreground_column_names = [input_column_names[i] for i, val in enumerate(binary_vector[:-1]) if val == 1] df = pd.concat([background_df[background_column_names], foreground_df[foreground_column_names]], axis=1) mechanism = foreground_mechanism if binary_vector[-1] else background_mechanism return mechanism.predict(df[input_column_names].values).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names) + 1, shapley_config) root_causes = input_column_names + ["f"] return pd.DataFrame(contributions, columns=root_causes) def unit_change_linear( background_mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_mechanism: LinearPredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a linear deterministic mechanism. :param background_mechanism: The linear background mechanism. :param background_df: The background data. :param foreground_mechanism: The linear foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) coeffs_total = background_mechanism.coefficients + foreground_mechanism.coefficients # p x 1 coeffs_diff = foreground_mechanism.coefficients - background_mechanism.coefficients # p x 1 input_total = foreground_df[input_column_names].to_numpy() + background_df[input_column_names].to_numpy() # n x p input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = 0.5 * np.einsum("ij,ki->ki", coeffs_total.reshape(-1, 1), input_diff) contribution_mechanism = 0.5 * np.einsum("ij,ki->k", coeffs_diff.reshape(-1, 1), input_total) contribution_df = pd.DataFrame(contribution_input, columns=input_column_names) contribution_df["f"] = contribution_mechanism # TODO: Handle the case where 'f' is an input column name return contribution_df def _check_if_input_columns_exist( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str] ) -> None: if not len(set(background_df.columns).intersection(input_column_names)) == len(input_column_names) or not len( set(foreground_df.columns).intersection(input_column_names) ) == len(input_column_names): raise ValueError("Input column names not found in either the background or the foreground data.")

"""This module provides the APIs for attributing the change in the output value of a deterministic mechanism for a statistical unit. """ from abc import abstractmethod from typing import List, Optional import numpy as np import pandas as pd from sklearn.linear_model._base import LinearModel from sklearn.utils.validation import check_is_fitted from dowhy.gcm.fcms import PredictionModel from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.shapley import ShapleyConfig, estimate_shapley_values class LinearPredictionModel: @property @abstractmethod def coefficients(self) -> np.ndarray: pass class SklearnLinearRegressionModel(SklearnRegressionModel, LinearPredictionModel): def __init__(self, sklearn_mdl: LinearModel) -> None: super(SklearnLinearRegressionModel, self).__init__(sklearn_mdl) @property def coefficients(self) -> np.ndarray: check_is_fitted(self.sklearn_model) return self.sklearn_model.coef_ def unit_change( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], background_mechanism: PredictionModel, foreground_mechanism: Optional[PredictionModel] = None, shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ This function attributes the change in the output value of a deterministic mechanism for a statistical unit to each input and optionally for the mechanism if `foreground_mechanism` is provided. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_df: The background dataset. :param foreground_df: The foreground dataset. :param input_column_names: The names of the input columns. :param background_mechanism: The background mechanism. If the mechanism does not change, then this mechanism is used for attribution. :param foreground_mechanism: The foreground mechanism. If provided, the method also attributes the output change to the change in the mechanism. :param shapley_config: The configuration for calculating Shapley values. :return: A dataframe containing the contributions of each input and optionally the mechanism to the change in the output values of the deterministic mechanism(s) for given inputs. """ if foreground_mechanism: if isinstance(background_mechanism, LinearPredictionModel): return unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, input_column_names ) else: return unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, input_column_names, shapley_config, ) if isinstance(background_mechanism, LinearPredictionModel): return unit_change_linear_input_only(background_mechanism, background_df, foreground_df, input_column_names) else: return unit_change_nonlinear_input_only( background_mechanism, background_df, foreground_df, input_column_names, shapley_config ) def unit_change_nonlinear( background_mechanism: PredictionModel, background_df: pd.DataFrame, foreground_mechanism: PredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a non-linear deterministic mechanism. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_mechanism: The background mechanism. :param background_df: The background data. :param foreground_mechanism: The foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(player_indicator: List[int]) -> np.ndarray: """The last cell in the binary vector represents the player 'mechanism'.""" input_arrays = [] for i, is_player_active in enumerate(player_indicator[:-1]): selected_df = foreground_df if is_player_active else background_df input_arrays.append(selected_df[input_column_names[i]].to_numpy()) mechanism = foreground_mechanism if player_indicator[-1] else background_mechanism return mechanism.predict(np.column_stack(input_arrays)).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names) + 1, shapley_config) root_causes = input_column_names + ["f"] return pd.DataFrame(contributions, columns=root_causes) def unit_change_linear( background_mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_mechanism: LinearPredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a linear deterministic mechanism. :param background_mechanism: The linear background mechanism. :param background_df: The background data. :param foreground_mechanism: The linear foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) coeffs_total = background_mechanism.coefficients + foreground_mechanism.coefficients # p x 1 coeffs_diff = foreground_mechanism.coefficients - background_mechanism.coefficients # p x 1 input_total = foreground_df[input_column_names].to_numpy() + background_df[input_column_names].to_numpy() # n x p input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = 0.5 * np.einsum("ij,ki->ki", coeffs_total.reshape(-1, 1), input_diff) contribution_mechanism = 0.5 * np.einsum("ij,ki->k", coeffs_diff.reshape(-1, 1), input_total) contribution_df = pd.DataFrame(contribution_input, columns=input_column_names) contribution_df["f"] = contribution_mechanism # TODO: Handle the case where 'f' is an input column name return contribution_df def unit_change_nonlinear_input_only( mechanism: PredictionModel, background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of each input to the change in the output values of a non-linear deterministic mechanism. The technical method is a modification of the attribution method described in the following research paper, without mechanism as a player: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param mechanism: The mechanism. :param background_df: The background data. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(player_indicator: List[int]) -> np.ndarray: input_arrays = [] for i, is_player_active in enumerate(player_indicator): selected_df = foreground_df if is_player_active else background_df input_arrays.append(selected_df[input_column_names[i]].to_numpy()) return mechanism.predict(np.column_stack(input_arrays)).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names), shapley_config) return pd.DataFrame(contributions, columns=input_column_names) def unit_change_linear_input_only( mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of each input to the change in the output values of a linear deterministic mechanism. :param mechanism: The linear mechanism. :param background_df: The background data. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = np.einsum("ij,ki->ki", mechanism.coefficients.reshape(-1, 1), input_diff) return pd.DataFrame(contribution_input, columns=input_column_names) def _check_if_input_columns_exist( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str] ) -> None: if not len(set(background_df.columns).intersection(input_column_names)) == len(input_column_names) or not len( set(foreground_df.columns).intersection(input_column_names) ) == len(input_column_names): raise ValueError("Input column names not found in either the background or the foreground data.")

kailashbuki

675cbc444cc422b007ba72fdf3303b328b123c48

ac047066326d0de3646f8461c0c5c4dd9826287c

Under a single method, a user still has to select an appropriate wrapper (`SklearnLinearRegressionModel` or `SklearnRegressionModel`) for sklearn models, and pass its object. At this point, just calling a more explicit API is better, no? It is also more transparent. A bit more theoretical argument: With `isinstance` pattern, if we add new model types in the future, we have to keep on adding conditions and change this one method. The two arguments `foreground_mechanism` and `background_mechanism` does not make sense anymore when `analyze_inputs_only` is set to True.

kailashbuki

py-why/dowhy

Add APIs for attributing unit change without a mechanism change

- Added two new APIs for attributing unit-level output changes when the mechanism does not change. Signed-off-by: Kailash <111277+kailashbuki@users.noreply.github.com>

2022-11-14 09:40:52+00:00

2022-11-14 21:51:34+00:00

dowhy/gcm/unit_change.py

"""This module provides the APIs for attributing the change in the output value of a deterministic mechanism for a statistical unit. """ from abc import abstractmethod from typing import List, Optional import numpy as np import pandas as pd from sklearn.linear_model._base import LinearModel from sklearn.utils.validation import check_is_fitted from dowhy.gcm.fcms import PredictionModel from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.shapley import ShapleyConfig, estimate_shapley_values class LinearPredictionModel: @property @abstractmethod def coefficients(self) -> np.ndarray: pass class SklearnLinearRegressionModel(SklearnRegressionModel, LinearPredictionModel): def __init__(self, sklearn_mdl: LinearModel) -> None: super(SklearnLinearRegressionModel, self).__init__(sklearn_mdl) @property def coefficients(self) -> np.ndarray: check_is_fitted(self.sklearn_model) return self.sklearn_model.coef_ def unit_change_nonlinear( background_mechanism: PredictionModel, background_df: pd.DataFrame, foreground_mechanism: PredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a non-linear deterministic mechanism. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_mechanism: The background mechanism. :param background_df: The background data. :param foreground_mechanism: The foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(binary_vector: List[int]) -> np.ndarray: """The last cell in the binary vector represents the player 'mechanism'.""" background_column_names = [input_column_names[i] for i, val in enumerate(binary_vector[:-1]) if val == 0] foreground_column_names = [input_column_names[i] for i, val in enumerate(binary_vector[:-1]) if val == 1] df = pd.concat([background_df[background_column_names], foreground_df[foreground_column_names]], axis=1) mechanism = foreground_mechanism if binary_vector[-1] else background_mechanism return mechanism.predict(df[input_column_names].values).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names) + 1, shapley_config) root_causes = input_column_names + ["f"] return pd.DataFrame(contributions, columns=root_causes) def unit_change_linear( background_mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_mechanism: LinearPredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a linear deterministic mechanism. :param background_mechanism: The linear background mechanism. :param background_df: The background data. :param foreground_mechanism: The linear foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) coeffs_total = background_mechanism.coefficients + foreground_mechanism.coefficients # p x 1 coeffs_diff = foreground_mechanism.coefficients - background_mechanism.coefficients # p x 1 input_total = foreground_df[input_column_names].to_numpy() + background_df[input_column_names].to_numpy() # n x p input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = 0.5 * np.einsum("ij,ki->ki", coeffs_total.reshape(-1, 1), input_diff) contribution_mechanism = 0.5 * np.einsum("ij,ki->k", coeffs_diff.reshape(-1, 1), input_total) contribution_df = pd.DataFrame(contribution_input, columns=input_column_names) contribution_df["f"] = contribution_mechanism # TODO: Handle the case where 'f' is an input column name return contribution_df def _check_if_input_columns_exist( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str] ) -> None: if not len(set(background_df.columns).intersection(input_column_names)) == len(input_column_names) or not len( set(foreground_df.columns).intersection(input_column_names) ) == len(input_column_names): raise ValueError("Input column names not found in either the background or the foreground data.")

"""This module provides the APIs for attributing the change in the output value of a deterministic mechanism for a statistical unit. """ from abc import abstractmethod from typing import List, Optional import numpy as np import pandas as pd from sklearn.linear_model._base import LinearModel from sklearn.utils.validation import check_is_fitted from dowhy.gcm.fcms import PredictionModel from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.shapley import ShapleyConfig, estimate_shapley_values class LinearPredictionModel: @property @abstractmethod def coefficients(self) -> np.ndarray: pass class SklearnLinearRegressionModel(SklearnRegressionModel, LinearPredictionModel): def __init__(self, sklearn_mdl: LinearModel) -> None: super(SklearnLinearRegressionModel, self).__init__(sklearn_mdl) @property def coefficients(self) -> np.ndarray: check_is_fitted(self.sklearn_model) return self.sklearn_model.coef_ def unit_change( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], background_mechanism: PredictionModel, foreground_mechanism: Optional[PredictionModel] = None, shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ This function attributes the change in the output value of a deterministic mechanism for a statistical unit to each input and optionally for the mechanism if `foreground_mechanism` is provided. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_df: The background dataset. :param foreground_df: The foreground dataset. :param input_column_names: The names of the input columns. :param background_mechanism: The background mechanism. If the mechanism does not change, then this mechanism is used for attribution. :param foreground_mechanism: The foreground mechanism. If provided, the method also attributes the output change to the change in the mechanism. :param shapley_config: The configuration for calculating Shapley values. :return: A dataframe containing the contributions of each input and optionally the mechanism to the change in the output values of the deterministic mechanism(s) for given inputs. """ if foreground_mechanism: if isinstance(background_mechanism, LinearPredictionModel): return unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, input_column_names ) else: return unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, input_column_names, shapley_config, ) if isinstance(background_mechanism, LinearPredictionModel): return unit_change_linear_input_only(background_mechanism, background_df, foreground_df, input_column_names) else: return unit_change_nonlinear_input_only( background_mechanism, background_df, foreground_df, input_column_names, shapley_config ) def unit_change_nonlinear( background_mechanism: PredictionModel, background_df: pd.DataFrame, foreground_mechanism: PredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a non-linear deterministic mechanism. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_mechanism: The background mechanism. :param background_df: The background data. :param foreground_mechanism: The foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(player_indicator: List[int]) -> np.ndarray: """The last cell in the binary vector represents the player 'mechanism'.""" input_arrays = [] for i, is_player_active in enumerate(player_indicator[:-1]): selected_df = foreground_df if is_player_active else background_df input_arrays.append(selected_df[input_column_names[i]].to_numpy()) mechanism = foreground_mechanism if player_indicator[-1] else background_mechanism return mechanism.predict(np.column_stack(input_arrays)).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names) + 1, shapley_config) root_causes = input_column_names + ["f"] return pd.DataFrame(contributions, columns=root_causes) def unit_change_linear( background_mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_mechanism: LinearPredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a linear deterministic mechanism. :param background_mechanism: The linear background mechanism. :param background_df: The background data. :param foreground_mechanism: The linear foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) coeffs_total = background_mechanism.coefficients + foreground_mechanism.coefficients # p x 1 coeffs_diff = foreground_mechanism.coefficients - background_mechanism.coefficients # p x 1 input_total = foreground_df[input_column_names].to_numpy() + background_df[input_column_names].to_numpy() # n x p input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = 0.5 * np.einsum("ij,ki->ki", coeffs_total.reshape(-1, 1), input_diff) contribution_mechanism = 0.5 * np.einsum("ij,ki->k", coeffs_diff.reshape(-1, 1), input_total) contribution_df = pd.DataFrame(contribution_input, columns=input_column_names) contribution_df["f"] = contribution_mechanism # TODO: Handle the case where 'f' is an input column name return contribution_df def unit_change_nonlinear_input_only( mechanism: PredictionModel, background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of each input to the change in the output values of a non-linear deterministic mechanism. The technical method is a modification of the attribution method described in the following research paper, without mechanism as a player: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param mechanism: The mechanism. :param background_df: The background data. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(player_indicator: List[int]) -> np.ndarray: input_arrays = [] for i, is_player_active in enumerate(player_indicator): selected_df = foreground_df if is_player_active else background_df input_arrays.append(selected_df[input_column_names[i]].to_numpy()) return mechanism.predict(np.column_stack(input_arrays)).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names), shapley_config) return pd.DataFrame(contributions, columns=input_column_names) def unit_change_linear_input_only( mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of each input to the change in the output values of a linear deterministic mechanism. :param mechanism: The linear mechanism. :param background_df: The background data. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = np.einsum("ij,ki->ki", mechanism.coefficients.reshape(-1, 1), input_diff) return pd.DataFrame(contribution_input, columns=input_column_names) def _check_if_input_columns_exist( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str] ) -> None: if not len(set(background_df.columns).intersection(input_column_names)) == len(input_column_names) or not len( set(foreground_df.columns).intersection(input_column_names) ) == len(input_column_names): raise ValueError("Input column names not found in either the background or the foreground data.")

kailashbuki

675cbc444cc422b007ba72fdf3303b328b123c48

ac047066326d0de3646f8461c0c5c4dd9826287c

> Under a single method, a user still has to select an appropriate wrapper (SklearnLinearRegressionModel or SklearnRegressionModel) for sklearn models, and pass its object That's right, one need to check if the model ```has_coefficients``` actually, since this is what you need in the linear solution. I see the concern here. However, it would probably simplify the usage seeing that, if we have ```has_coefficients```, then the ```_linear``` version represents the closed-form solution that avoids the Shapley estimation. In that sense, there is no reason to use the ```_nonlinear``` version with a linear model. I guess the question here is: Do we want to go a route where the methods automatically optimize the computation based on the model type (which requires ugly things like ```if isinstance(x, y)```) or should this be the responsibility of the user?

bloebp

py-why/dowhy

Add APIs for attributing unit change without a mechanism change

- Added two new APIs for attributing unit-level output changes when the mechanism does not change. Signed-off-by: Kailash <111277+kailashbuki@users.noreply.github.com>

2022-11-14 09:40:52+00:00

2022-11-14 21:51:34+00:00

dowhy/gcm/unit_change.py

"""This module provides the APIs for attributing the change in the output value of a deterministic mechanism for a statistical unit. """ from abc import abstractmethod from typing import List, Optional import numpy as np import pandas as pd from sklearn.linear_model._base import LinearModel from sklearn.utils.validation import check_is_fitted from dowhy.gcm.fcms import PredictionModel from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.shapley import ShapleyConfig, estimate_shapley_values class LinearPredictionModel: @property @abstractmethod def coefficients(self) -> np.ndarray: pass class SklearnLinearRegressionModel(SklearnRegressionModel, LinearPredictionModel): def __init__(self, sklearn_mdl: LinearModel) -> None: super(SklearnLinearRegressionModel, self).__init__(sklearn_mdl) @property def coefficients(self) -> np.ndarray: check_is_fitted(self.sklearn_model) return self.sklearn_model.coef_ def unit_change_nonlinear( background_mechanism: PredictionModel, background_df: pd.DataFrame, foreground_mechanism: PredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a non-linear deterministic mechanism. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_mechanism: The background mechanism. :param background_df: The background data. :param foreground_mechanism: The foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(binary_vector: List[int]) -> np.ndarray: """The last cell in the binary vector represents the player 'mechanism'.""" background_column_names = [input_column_names[i] for i, val in enumerate(binary_vector[:-1]) if val == 0] foreground_column_names = [input_column_names[i] for i, val in enumerate(binary_vector[:-1]) if val == 1] df = pd.concat([background_df[background_column_names], foreground_df[foreground_column_names]], axis=1) mechanism = foreground_mechanism if binary_vector[-1] else background_mechanism return mechanism.predict(df[input_column_names].values).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names) + 1, shapley_config) root_causes = input_column_names + ["f"] return pd.DataFrame(contributions, columns=root_causes) def unit_change_linear( background_mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_mechanism: LinearPredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a linear deterministic mechanism. :param background_mechanism: The linear background mechanism. :param background_df: The background data. :param foreground_mechanism: The linear foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) coeffs_total = background_mechanism.coefficients + foreground_mechanism.coefficients # p x 1 coeffs_diff = foreground_mechanism.coefficients - background_mechanism.coefficients # p x 1 input_total = foreground_df[input_column_names].to_numpy() + background_df[input_column_names].to_numpy() # n x p input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = 0.5 * np.einsum("ij,ki->ki", coeffs_total.reshape(-1, 1), input_diff) contribution_mechanism = 0.5 * np.einsum("ij,ki->k", coeffs_diff.reshape(-1, 1), input_total) contribution_df = pd.DataFrame(contribution_input, columns=input_column_names) contribution_df["f"] = contribution_mechanism # TODO: Handle the case where 'f' is an input column name return contribution_df def _check_if_input_columns_exist( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str] ) -> None: if not len(set(background_df.columns).intersection(input_column_names)) == len(input_column_names) or not len( set(foreground_df.columns).intersection(input_column_names) ) == len(input_column_names): raise ValueError("Input column names not found in either the background or the foreground data.")

"""This module provides the APIs for attributing the change in the output value of a deterministic mechanism for a statistical unit. """ from abc import abstractmethod from typing import List, Optional import numpy as np import pandas as pd from sklearn.linear_model._base import LinearModel from sklearn.utils.validation import check_is_fitted from dowhy.gcm.fcms import PredictionModel from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.shapley import ShapleyConfig, estimate_shapley_values class LinearPredictionModel: @property @abstractmethod def coefficients(self) -> np.ndarray: pass class SklearnLinearRegressionModel(SklearnRegressionModel, LinearPredictionModel): def __init__(self, sklearn_mdl: LinearModel) -> None: super(SklearnLinearRegressionModel, self).__init__(sklearn_mdl) @property def coefficients(self) -> np.ndarray: check_is_fitted(self.sklearn_model) return self.sklearn_model.coef_ def unit_change( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], background_mechanism: PredictionModel, foreground_mechanism: Optional[PredictionModel] = None, shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ This function attributes the change in the output value of a deterministic mechanism for a statistical unit to each input and optionally for the mechanism if `foreground_mechanism` is provided. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_df: The background dataset. :param foreground_df: The foreground dataset. :param input_column_names: The names of the input columns. :param background_mechanism: The background mechanism. If the mechanism does not change, then this mechanism is used for attribution. :param foreground_mechanism: The foreground mechanism. If provided, the method also attributes the output change to the change in the mechanism. :param shapley_config: The configuration for calculating Shapley values. :return: A dataframe containing the contributions of each input and optionally the mechanism to the change in the output values of the deterministic mechanism(s) for given inputs. """ if foreground_mechanism: if isinstance(background_mechanism, LinearPredictionModel): return unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, input_column_names ) else: return unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, input_column_names, shapley_config, ) if isinstance(background_mechanism, LinearPredictionModel): return unit_change_linear_input_only(background_mechanism, background_df, foreground_df, input_column_names) else: return unit_change_nonlinear_input_only( background_mechanism, background_df, foreground_df, input_column_names, shapley_config ) def unit_change_nonlinear( background_mechanism: PredictionModel, background_df: pd.DataFrame, foreground_mechanism: PredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a non-linear deterministic mechanism. The technical method is described in the following research paper: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param background_mechanism: The background mechanism. :param background_df: The background data. :param foreground_mechanism: The foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(player_indicator: List[int]) -> np.ndarray: """The last cell in the binary vector represents the player 'mechanism'.""" input_arrays = [] for i, is_player_active in enumerate(player_indicator[:-1]): selected_df = foreground_df if is_player_active else background_df input_arrays.append(selected_df[input_column_names[i]].to_numpy()) mechanism = foreground_mechanism if player_indicator[-1] else background_mechanism return mechanism.predict(np.column_stack(input_arrays)).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names) + 1, shapley_config) root_causes = input_column_names + ["f"] return pd.DataFrame(contributions, columns=root_causes) def unit_change_linear( background_mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_mechanism: LinearPredictionModel, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of mechanism and each input to the change in the output values of a linear deterministic mechanism. :param background_mechanism: The linear background mechanism. :param background_df: The background data. :param foreground_mechanism: The linear foreground mechanism. :param foreground_df: The foreground data. :param input_column_names: The names of the input columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) coeffs_total = background_mechanism.coefficients + foreground_mechanism.coefficients # p x 1 coeffs_diff = foreground_mechanism.coefficients - background_mechanism.coefficients # p x 1 input_total = foreground_df[input_column_names].to_numpy() + background_df[input_column_names].to_numpy() # n x p input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = 0.5 * np.einsum("ij,ki->ki", coeffs_total.reshape(-1, 1), input_diff) contribution_mechanism = 0.5 * np.einsum("ij,ki->k", coeffs_diff.reshape(-1, 1), input_total) contribution_df = pd.DataFrame(contribution_input, columns=input_column_names) contribution_df["f"] = contribution_mechanism # TODO: Handle the case where 'f' is an input column name return contribution_df def unit_change_nonlinear_input_only( mechanism: PredictionModel, background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], shapley_config: Optional[ShapleyConfig] = None, ) -> pd.DataFrame: """ Calculates the contributions of each input to the change in the output values of a non-linear deterministic mechanism. The technical method is a modification of the attribution method described in the following research paper, without mechanism as a player: Kailash Budhathoki, George Michailidis, Dominik Janzing. *Explaining the root causes of unit-level changes*. arXiv, 2022. :param mechanism: The mechanism. :param background_df: The background data. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :param shapley_config: The configuration for calculating Shapley values. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) def payoff(player_indicator: List[int]) -> np.ndarray: input_arrays = [] for i, is_player_active in enumerate(player_indicator): selected_df = foreground_df if is_player_active else background_df input_arrays.append(selected_df[input_column_names[i]].to_numpy()) return mechanism.predict(np.column_stack(input_arrays)).flatten() contributions = estimate_shapley_values(payoff, len(input_column_names), shapley_config) return pd.DataFrame(contributions, columns=input_column_names) def unit_change_linear_input_only( mechanism: LinearPredictionModel, background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str], ) -> pd.DataFrame: """ Calculates the contributions of each input to the change in the output values of a linear deterministic mechanism. :param mechanism: The linear mechanism. :param background_df: The background data. :param foreground_df: The foreground data. :param input_column_names: The names of the input (features) columns in both dataframes. :return: A pandas dataframe with attributions to each cause for the change in each output row of provided dataframes. """ _check_if_input_columns_exist(background_df, foreground_df, input_column_names) input_diff = foreground_df[input_column_names].to_numpy() - background_df[input_column_names].to_numpy() # n x p contribution_input = np.einsum("ij,ki->ki", mechanism.coefficients.reshape(-1, 1), input_diff) return pd.DataFrame(contribution_input, columns=input_column_names) def _check_if_input_columns_exist( background_df: pd.DataFrame, foreground_df: pd.DataFrame, input_column_names: List[str] ) -> None: if not len(set(background_df.columns).intersection(input_column_names)) == len(input_column_names) or not len( set(foreground_df.columns).intersection(input_column_names) ) == len(input_column_names): raise ValueError("Input column names not found in either the background or the foreground data.")

kailashbuki

675cbc444cc422b007ba72fdf3303b328b123c48

ac047066326d0de3646f8461c0c5c4dd9826287c

Force pushed a single helper API for all those four APIs.

kailashbuki

py-why/dowhy

Add APIs for attributing unit change without a mechanism change

- Added two new APIs for attributing unit-level output changes when the mechanism does not change. Signed-off-by: Kailash <111277+kailashbuki@users.noreply.github.com>

2022-11-14 09:40:52+00:00

2022-11-14 21:51:34+00:00

tests/gcm/test_unit_change.py

import numpy as np import pandas as pd import pytest from flaky import flaky from sklearn.ensemble import RandomForestRegressor as RFR from sklearn.exceptions import NotFittedError from sklearn.linear_model import LinearRegression from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.unit_change import SklearnLinearRegressionModel, unit_change_linear, unit_change_nonlinear @flaky(max_runs=5) def test_given_fitted_linear_mechanisms_with_output_change_when_evaluate_unit_change_linear_method_then_returns_correct_attributions(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) expected_contributions = pd.DataFrame( data=dict( A=(3 + 2) * (A2 - A1) / 2, B=(2 + 3) * (B2 - B1) / 2, f=(A1 + A2) * (3 - 2) / 2 + (B1 + B2) * (2 - 3) / 2 ) ) np.testing.assert_array_almost_equal(actual_contributions.to_numpy(), expected_contributions.to_numpy(), decimal=1) @flaky(max_runs=5) def test_given_fitted_linear_mechanisms_with_output_change_when_evaluate_unit_change_linear_and_nonlinear_methods_then_attributions_are_consistent(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) expected_contributions = unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) np.testing.assert_array_almost_equal(actual_contributions.to_numpy(), expected_contributions.to_numpy(), decimal=1) def test_given_unfitted_mechanisms_when_evaluate_unit_change_methods_then_raises_exception(): with pytest.raises(NotFittedError): unit_change_linear( SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear( SklearnRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear( SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) def test_given_fitted_nonlinnear_mechanisms_when_evaluate_unit_change_linear_method_then_raises_exception(): with pytest.raises(AttributeError): unit_change_linear( SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], )

import numpy as np import pandas as pd import pytest from flaky import flaky from sklearn.ensemble import RandomForestRegressor as RFR from sklearn.exceptions import NotFittedError from sklearn.linear_model import LinearRegression from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.unit_change import ( SklearnLinearRegressionModel, unit_change, unit_change_linear, unit_change_linear_input_only, unit_change_nonlinear, unit_change_nonlinear_input_only, ) @flaky(max_runs=5) def test_given_fitted_linear_mechanisms_with_output_change_when_evaluate_unit_change_linear_method_then_returns_correct_attributions(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) expected_contributions = pd.DataFrame( data=dict( A=(3 + 2) * (A2 - A1) / 2, B=(2 + 3) * (B2 - B1) / 2, f=(A1 + A2) * (3 - 2) / 2 + (B1 + B2) * (2 - 3) / 2 ) ) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) @flaky(max_runs=5) def test_given_fitted_linear_mechanisms_with_output_change_when_evaluate_unit_change_linear_and_nonlinear_methods_then_attributions_are_consistent(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) expected_contributions = unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) def test_given_unfitted_mechanisms_when_evaluate_unit_change_methods_then_raises_exception(): with pytest.raises(NotFittedError): unit_change_linear( SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear( SklearnRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear( SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) def test_given_fitted_nonlinnear_mechanisms_when_evaluate_unit_change_linear_method_then_raises_exception(): with pytest.raises(AttributeError): unit_change_linear( SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) @flaky(max_runs=5) def test_given_fitted_mechanisms_with_no_input_change_when_evaluate_unit_change_input_only_methods_then_returns_zero_attributions(): num_rows = 100 A = np.random.normal(size=num_rows) B = np.random.normal(size=num_rows) C = 3 * A + 2 * B background_df = pd.DataFrame(data=dict(A=A, B=B, C=C)) foreground_df = pd.DataFrame(data=dict(A=A, B=B, C=C)) actual_contributions = unit_change_nonlinear_input_only( SklearnRegressionModel(RFR().fit(np.column_stack((A, B)), C)), background_df, foreground_df, ["A", "B"], ) expected_contributions = pd.DataFrame(data=dict(A=np.zeros(num_rows), B=np.zeros(num_rows))) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) @flaky(max_runs=5) def test_given_fitted_linear_mechanism_with_input_change_when_evaluate_unit_change_linear_input_only_then_returns_correct_attributions(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 3 * A1 + 2 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1, C=C1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2, C=C2)) fitted_linear_reg = LinearRegression() fitted_linear_reg.coef_ = np.array([3, 2]) actual_contributions = unit_change_linear_input_only( SklearnLinearRegressionModel(fitted_linear_reg), background_df, foreground_df, ["A", "B"] ) expected_contributions = pd.DataFrame(data=dict(A=3 * (A2 - A1), B=2 * (B2 - B1))) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) @flaky(max_runs=5) def test_given_fitted_linear_mechanism_with_input_change_when_evaluate_unit_change_input_only_methods_then_attributions_are_consistent(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 3 * A1 + 2 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1, C=C1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2, C=C2)) mechanism = SklearnLinearRegressionModel(LinearRegression().fit(np.column_stack((A1, B1)), C1)) actual_contributions = unit_change_nonlinear_input_only(mechanism, background_df, foreground_df, ["A", "B"]) expected_contributions = unit_change_linear_input_only(mechanism, background_df, foreground_df, ["A", "B"]) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) def test_given_unfitted_mechanisms_when_evaluate_unit_change_input_only_methods_then_raises_exception(): with pytest.raises(NotFittedError): unit_change_linear_input_only( SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear_input_only( SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear_input_only( SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) def test_given_fitted_nonlinnear_mechanism_when_evaluate_unit_change_linear_input_only_method_then_raises_exception(): with pytest.raises(AttributeError): unit_change_linear_input_only( SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) @flaky(max_runs=5) def test_given_single_mechanism_with_default_optional_parameters_when_evaluate_unit_change_then_returns_correct_attributions_to_input_only(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) # C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) mechanism = SklearnLinearRegressionModel(LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1)) actual_contributions = unit_change(background_df, foreground_df, ["A", "B"], mechanism) expected_contributions = unit_change_linear_input_only(mechanism, background_df, foreground_df, ["A", "B"]) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) mechanism = SklearnRegressionModel(RFR().fit(np.column_stack((A1, B1)), C1)) actual_contributions = unit_change(background_df, foreground_df, ["A", "B"], mechanism) expected_contributions = unit_change_nonlinear_input_only(mechanism, background_df, foreground_df, ["A", "B"]) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) @flaky(max_runs=5) def test_given_two_mechanisms_when_evaluate_unit_change_then_returns_correct_attributions_to_both_mechanism_and_input(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change( background_df, foreground_df, ["A", "B"], background_mechanism, foreground_mechanism ) expected_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) background_mechanism = SklearnRegressionModel(RFR().fit(np.column_stack((A1, B1)), C1)) foreground_mechanism = SklearnRegressionModel(RFR().fit(np.column_stack((A2, B2)), C2)) actual_contributions = unit_change( background_df, foreground_df, ["A", "B"], background_mechanism, foreground_mechanism ) expected_contributions = unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1)

kailashbuki

675cbc444cc422b007ba72fdf3303b328b123c48

ac047066326d0de3646f8461c0c5c4dd9826287c

It looks like you don't really need `to_numpy()` as `assert_array_almost_equal` does this for you.

petergtz

py-why/dowhy

Add APIs for attributing unit change without a mechanism change

- Added two new APIs for attributing unit-level output changes when the mechanism does not change. Signed-off-by: Kailash <111277+kailashbuki@users.noreply.github.com>

2022-11-14 09:40:52+00:00

2022-11-14 21:51:34+00:00

tests/gcm/test_unit_change.py

import numpy as np import pandas as pd import pytest from flaky import flaky from sklearn.ensemble import RandomForestRegressor as RFR from sklearn.exceptions import NotFittedError from sklearn.linear_model import LinearRegression from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.unit_change import SklearnLinearRegressionModel, unit_change_linear, unit_change_nonlinear @flaky(max_runs=5) def test_given_fitted_linear_mechanisms_with_output_change_when_evaluate_unit_change_linear_method_then_returns_correct_attributions(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) expected_contributions = pd.DataFrame( data=dict( A=(3 + 2) * (A2 - A1) / 2, B=(2 + 3) * (B2 - B1) / 2, f=(A1 + A2) * (3 - 2) / 2 + (B1 + B2) * (2 - 3) / 2 ) ) np.testing.assert_array_almost_equal(actual_contributions.to_numpy(), expected_contributions.to_numpy(), decimal=1) @flaky(max_runs=5) def test_given_fitted_linear_mechanisms_with_output_change_when_evaluate_unit_change_linear_and_nonlinear_methods_then_attributions_are_consistent(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) expected_contributions = unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) np.testing.assert_array_almost_equal(actual_contributions.to_numpy(), expected_contributions.to_numpy(), decimal=1) def test_given_unfitted_mechanisms_when_evaluate_unit_change_methods_then_raises_exception(): with pytest.raises(NotFittedError): unit_change_linear( SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear( SklearnRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear( SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) def test_given_fitted_nonlinnear_mechanisms_when_evaluate_unit_change_linear_method_then_raises_exception(): with pytest.raises(AttributeError): unit_change_linear( SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], )

import numpy as np import pandas as pd import pytest from flaky import flaky from sklearn.ensemble import RandomForestRegressor as RFR from sklearn.exceptions import NotFittedError from sklearn.linear_model import LinearRegression from dowhy.gcm.ml.regression import SklearnRegressionModel from dowhy.gcm.unit_change import ( SklearnLinearRegressionModel, unit_change, unit_change_linear, unit_change_linear_input_only, unit_change_nonlinear, unit_change_nonlinear_input_only, ) @flaky(max_runs=5) def test_given_fitted_linear_mechanisms_with_output_change_when_evaluate_unit_change_linear_method_then_returns_correct_attributions(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) expected_contributions = pd.DataFrame( data=dict( A=(3 + 2) * (A2 - A1) / 2, B=(2 + 3) * (B2 - B1) / 2, f=(A1 + A2) * (3 - 2) / 2 + (B1 + B2) * (2 - 3) / 2 ) ) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) @flaky(max_runs=5) def test_given_fitted_linear_mechanisms_with_output_change_when_evaluate_unit_change_linear_and_nonlinear_methods_then_attributions_are_consistent(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) expected_contributions = unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) def test_given_unfitted_mechanisms_when_evaluate_unit_change_methods_then_raises_exception(): with pytest.raises(NotFittedError): unit_change_linear( SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear( SklearnRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear( SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) def test_given_fitted_nonlinnear_mechanisms_when_evaluate_unit_change_linear_method_then_raises_exception(): with pytest.raises(AttributeError): unit_change_linear( SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) @flaky(max_runs=5) def test_given_fitted_mechanisms_with_no_input_change_when_evaluate_unit_change_input_only_methods_then_returns_zero_attributions(): num_rows = 100 A = np.random.normal(size=num_rows) B = np.random.normal(size=num_rows) C = 3 * A + 2 * B background_df = pd.DataFrame(data=dict(A=A, B=B, C=C)) foreground_df = pd.DataFrame(data=dict(A=A, B=B, C=C)) actual_contributions = unit_change_nonlinear_input_only( SklearnRegressionModel(RFR().fit(np.column_stack((A, B)), C)), background_df, foreground_df, ["A", "B"], ) expected_contributions = pd.DataFrame(data=dict(A=np.zeros(num_rows), B=np.zeros(num_rows))) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) @flaky(max_runs=5) def test_given_fitted_linear_mechanism_with_input_change_when_evaluate_unit_change_linear_input_only_then_returns_correct_attributions(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 3 * A1 + 2 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1, C=C1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2, C=C2)) fitted_linear_reg = LinearRegression() fitted_linear_reg.coef_ = np.array([3, 2]) actual_contributions = unit_change_linear_input_only( SklearnLinearRegressionModel(fitted_linear_reg), background_df, foreground_df, ["A", "B"] ) expected_contributions = pd.DataFrame(data=dict(A=3 * (A2 - A1), B=2 * (B2 - B1))) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) @flaky(max_runs=5) def test_given_fitted_linear_mechanism_with_input_change_when_evaluate_unit_change_input_only_methods_then_attributions_are_consistent(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 3 * A1 + 2 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1, C=C1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2, C=C2)) mechanism = SklearnLinearRegressionModel(LinearRegression().fit(np.column_stack((A1, B1)), C1)) actual_contributions = unit_change_nonlinear_input_only(mechanism, background_df, foreground_df, ["A", "B"]) expected_contributions = unit_change_linear_input_only(mechanism, background_df, foreground_df, ["A", "B"]) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) def test_given_unfitted_mechanisms_when_evaluate_unit_change_input_only_methods_then_raises_exception(): with pytest.raises(NotFittedError): unit_change_linear_input_only( SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear_input_only( SklearnLinearRegressionModel(LinearRegression()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) with pytest.raises(NotFittedError): unit_change_nonlinear_input_only( SklearnRegressionModel(RFR()), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) def test_given_fitted_nonlinnear_mechanism_when_evaluate_unit_change_linear_input_only_method_then_raises_exception(): with pytest.raises(AttributeError): unit_change_linear_input_only( SklearnRegressionModel(RFR().fit(np.random.normal(size=(100, 2)), np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), pd.DataFrame(data=dict(A=np.random.normal(size=100), B=np.random.normal(size=100))), ["A", "B"], ) @flaky(max_runs=5) def test_given_single_mechanism_with_default_optional_parameters_when_evaluate_unit_change_then_returns_correct_attributions_to_input_only(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) # C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) mechanism = SklearnLinearRegressionModel(LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1)) actual_contributions = unit_change(background_df, foreground_df, ["A", "B"], mechanism) expected_contributions = unit_change_linear_input_only(mechanism, background_df, foreground_df, ["A", "B"]) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) mechanism = SklearnRegressionModel(RFR().fit(np.column_stack((A1, B1)), C1)) actual_contributions = unit_change(background_df, foreground_df, ["A", "B"], mechanism) expected_contributions = unit_change_nonlinear_input_only(mechanism, background_df, foreground_df, ["A", "B"]) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) @flaky(max_runs=5) def test_given_two_mechanisms_when_evaluate_unit_change_then_returns_correct_attributions_to_both_mechanism_and_input(): num_rows = 100 A1 = np.random.normal(size=num_rows) B1 = np.random.normal(size=num_rows) C1 = 2 * A1 + 3 * B1 A2 = np.random.normal(size=num_rows) B2 = np.random.normal(size=num_rows) C2 = 3 * A2 + 2 * B2 background_df = pd.DataFrame(data=dict(A=A1, B=B1)) foreground_df = pd.DataFrame(data=dict(A=A2, B=B2)) background_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A1, B1)), C1) ) foreground_mechanism = SklearnLinearRegressionModel( LinearRegression(fit_intercept=False).fit(np.column_stack((A2, B2)), C2) ) actual_contributions = unit_change( background_df, foreground_df, ["A", "B"], background_mechanism, foreground_mechanism ) expected_contributions = unit_change_linear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1) background_mechanism = SklearnRegressionModel(RFR().fit(np.column_stack((A1, B1)), C1)) foreground_mechanism = SklearnRegressionModel(RFR().fit(np.column_stack((A2, B2)), C2)) actual_contributions = unit_change( background_df, foreground_df, ["A", "B"], background_mechanism, foreground_mechanism ) expected_contributions = unit_change_nonlinear( background_mechanism, background_df, foreground_mechanism, foreground_df, ["A", "B"] ) np.testing.assert_array_almost_equal(actual_contributions, expected_contributions, decimal=1)

kailashbuki

675cbc444cc422b007ba72fdf3303b328b123c48

ac047066326d0de3646f8461c0c5c4dd9826287c

Something I know now. Thank you. Force pushing the fix.

kailashbuki

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/example_notebooks/DoWhy-The Causal Story Behind Hotel Booking Cancellations.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exploring Causes of Hotel Booking Cancellations" ] }, { "attachments": { "Screenshot%20from%202020-09-29%2019-08-50.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "We consider what factors cause a hotel booking to be cancelled. This analysis is based on a hotel bookings dataset from [Antonio, Almeida and Nunes (2019)](https://www.sciencedirect.com/science/article/pii/S2352340918315191). On GitHub, the dataset is available at [rfordatascience/tidytuesday](https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-02-11/readme.md). \n", "\n", "There can be different reasons for why a booking is cancelled. A customer may have requested something that was not available (e.g., car parking), a customer may have found later that the hotel did not meet their requirements, or a customer may have simply cancelled their entire trip. Some of these like car parking are actionable by the hotel whereas others like trip cancellation are outside the hotel's control. In any case, we would like to better understand which of these factors cause booking cancellations. \n", "\n", "The gold standard of finding this out would be to use experiments such as *Randomized Controlled Trials* wherein each customer is randomly assigned to one of the two categories i.e. each customer is either assigned a car parking or not. However, such an experiment can be too costly and also unethical in some cases (for example, a hotel would start losing its reputation if people learn that its randomly assigning people to different level of service). \n", "\n", "Can we somehow answer our query using only observational data or data that has been collected in the past?\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%reload_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Config dict to set the logging level\n", "import logging.config\n", "DEFAULT_LOGGING = {\n", " 'version': 1,\n", " 'disable_existing_loggers': False,\n", " 'loggers': {\n", " '': {\n", " 'level': 'INFO',\n", " },\n", " }\n", "}\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "# Disabling warnings output\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning, ConvergenceWarning\n", "warnings.filterwarnings(action='ignore', category=DataConversionWarning)\n", "warnings.filterwarnings(action='ignore', category=ConvergenceWarning)\n", "warnings.filterwarnings(action='ignore', category=UserWarning)\n", "\n", "#!pip install dowhy\n", "import dowhy\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Description\n", "For a quick glance of the features and their descriptions the reader is referred here.\n", "https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-02-11/readme.md" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = pd.read_csv('https://raw.githubusercontent.com/Sid-darthvader/DoWhy-The-Causal-Story-Behind-Hotel-Booking-Cancellations/master/hotel_bookings.csv')\n", "dataset.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Feature Engineering\n", "\n", "Lets create some new and meaningful features so as to reduce the dimensionality of the dataset. \n", "- **Total Stay** = stays_in_weekend_nights + stays_in_week_nights\n", "- **Guests** = adults + children + babies\n", "- **Different_room_assigned** = 1 if reserved_room_type & assigned_room_type are different, 0 otherwise." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Total stay in nights\n", "dataset['total_stay'] = dataset['stays_in_week_nights']+dataset['stays_in_weekend_nights']\n", "# Total number of guests\n", "dataset['guests'] = dataset['adults']+dataset['children'] +dataset['babies']\n", "# Creating the different_room_assigned feature\n", "dataset['different_room_assigned']=0\n", "slice_indices =dataset['reserved_room_type']!=dataset['assigned_room_type']\n", "dataset.loc[slice_indices,'different_room_assigned']=1\n", "# Deleting older features\n", "dataset = dataset.drop(['stays_in_week_nights','stays_in_weekend_nights','adults','children','babies'\n", " ,'reserved_room_type','assigned_room_type'],axis=1)\n", "dataset.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also remove other columns that either contain NULL values or have too many unique values (e.g., agent ID). We also impute missing values of the `country` column with the most frequent country. We remove `distribution_channel` since it has a high overlap with `market_segment`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset.isnull().sum() # Country,Agent,Company contain 488,16340,112593 missing entries \n", "dataset = dataset.drop(['agent','company'],axis=1)\n", "# Replacing missing countries with most freqently occuring countries\n", "dataset['country']= dataset['country'].fillna(dataset['country'].mode()[0])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = dataset.drop(['reservation_status','reservation_status_date','arrival_date_day_of_month'],axis=1)\n", "dataset = dataset.drop(['arrival_date_year'],axis=1)\n", "dataset = dataset.drop(['distribution_channel'], axis=1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Replacing 1 by True and 0 by False for the experiment and outcome variables\n", "dataset['different_room_assigned']= dataset['different_room_assigned'].replace(1,True)\n", "dataset['different_room_assigned']= dataset['different_room_assigned'].replace(0,False)\n", "dataset['is_canceled']= dataset['is_canceled'].replace(1,True)\n", "dataset['is_canceled']= dataset['is_canceled'].replace(0,False)\n", "dataset.dropna(inplace=True)\n", "print(dataset.columns)\n", "dataset.iloc[:, 5:20].head(100)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = dataset[dataset.deposit_type==\"No Deposit\"]\n", "dataset.groupby(['deposit_type','is_canceled']).count()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset_copy = dataset.copy(deep=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating Expected Counts\n", "Since the number of number of cancellations and the number of times a different room was assigned is heavily imbalanced, we first choose 1000 observations at random to see that in how many cases do the variables; *'is_cancelled'* & *'different_room_assigned'* attain the same values. This whole process is then repeated 10000 times and the expected count turns out to be near 50% (i.e. the probability of these two variables attaining the same value at random).\n", "So statistically speaking, we have no definite conclusion at this stage. Thus assigning rooms different to what a customer had reserved during his booking earlier, may or may not lead to him/her cancelling that booking." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset.sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now consider the scenario when there were no booking changes and recalculate the expected count." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Expected Count when there are no booking changes \n", "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset[dataset[\"booking_changes\"]==0].sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the 2nd case, we take the scenario when there were booking changes(>0) and recalculate the expected count." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Expected Count when there are booking changes = 66.4%\n", "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset[dataset[\"booking_changes\"]>0].sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is definitely some change happening when the number of booking changes are non-zero. So it gives us a hint that *Booking Changes* may be affecting room cancellation.\n", "\n", "But is *Booking Changes* the only confounding variable? What if there were some unobserved confounders, regarding which we have no information(feature) present in our dataset. Would we still be able to make the same claims as before?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using DoWhy to estimate the causal effect" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step-1. Create a Causal Graph\n", "Represent your prior knowledge about the predictive modelling problem as a CI graph using assumptions. Don't worry, you need not specify the full graph at this stage. Even a partial graph would be enough and the rest can be figured out by *DoWhy* ;-)\n", "\n", "Here are a list of assumptions that have then been translated into a Causal Diagram:-\n", "\n", "- *Market Segment* has 2 levels, “TA” refers to the “Travel Agents” and “TO” means “Tour Operators” so it should affect the Lead Time (which is simply the number of days between booking and arrival).\n", "- *Country* would also play a role in deciding whether a person books early or not (hence more *Lead Time*) and what type of *Meal* a person would prefer.\n", "- *Lead Time* would definitely affected the number of *Days in Waitlist* (There are lesser chances of finding a reservation if you’re booking late). Additionally, higher *Lead Times* can also lead to *Cancellations*.\n", "- The number of *Days in Waitlist*, the *Total Stay* in nights and the number of *Guests* might affect whether the booking is cancelled or retained.\n", "- *Previous Booking Retentions* would affect whether a customer is a or not. Additionally, both of these variables would affect whether the booking get *cancelled* or not (Ex- A customer who has retained his past 5 bookings in the past has a higher chance of retaining this one also. Similarly a person who has been cancelling this booking has a higher chance of repeating the same).\n", "- *Booking Changes* would affect whether the customer is assigned a *different room* or not which might also lead to *cancellation*.\n", "- Finally, the number of *Booking Changes* being the only variable affecting *Treatment* and *Outcome* is highly unlikely and its possible that there might be some *Unobsevered Confounders*, regarding which we have no information being captured in our data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pygraphviz\n", "causal_graph = \"\"\"digraph {\n", "different_room_assigned[label=\"Different Room Assigned\"];\n", "is_canceled[label=\"Booking Cancelled\"];\n", "booking_changes[label=\"Booking Changes\"];\n", "previous_bookings_not_canceled[label=\"Previous Booking Retentions\"];\n", "days_in_waiting_list[label=\"Days in Waitlist\"];\n", "lead_time[label=\"Lead Time\"];\n", "market_segment[label=\"Market Segment\"];\n", "country[label=\"Country\"];\n", "U[label=\"Unobserved Confounders\",observed=\"no\"];\n", "is_repeated_guest;\n", "total_stay;\n", "guests;\n", "meal;\n", "hotel;\n", "U->{different_room_assigned,required_car_parking_spaces,guests,total_stay,total_of_special_requests};\n", "market_segment -> lead_time;\n", "lead_time->is_canceled; country -> lead_time;\n", "different_room_assigned -> is_canceled;\n", "country->meal;\n", "lead_time -> days_in_waiting_list;\n", "days_in_waiting_list ->{is_canceled,different_room_assigned};\n", "previous_bookings_not_canceled -> is_canceled;\n", "previous_bookings_not_canceled -> is_repeated_guest;\n", "is_repeated_guest -> {different_room_assigned,is_canceled};\n", "total_stay -> is_canceled;\n", "guests -> is_canceled;\n", "booking_changes -> different_room_assigned; booking_changes -> is_canceled; \n", "hotel -> {different_room_assigned,is_canceled};\n", "required_car_parking_spaces -> is_canceled;\n", "total_of_special_requests -> {booking_changes,is_canceled};\n", "country->{hotel, required_car_parking_spaces,total_of_special_requests};\n", "market_segment->{hotel, required_car_parking_spaces,total_of_special_requests};\n", "}\"\"\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the *Treatment* is assigning the same type of room reserved by the customer during Booking. *Outcome* would be whether the booking was cancelled or not.\n", "*Common Causes* represent the variables that according to us have a causal affect on both *Outcome* and *Treatment*.\n", "As per our causal assumptions, the 2 variables satisfying this criteria are *Booking Changes* and the *Unobserved Confounders*.\n", "So if we are not specifying the graph explicitly (Not Recommended!), one can also provide these as parameters in the function mentioned below.\n", "\n", "To aid in identification of causal effect, we remove the unobserved confounder node from the graph. (To check, you can use the original graph and run the following code. The `identify_effect` method will find that the effect cannot be identified.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model= dowhy.CausalModel(\n", " data = dataset,\n", " graph=causal_graph.replace(\"\\n\", \" \"),\n", " treatment=\"different_room_assigned\",\n", " outcome='is_canceled')\n", "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step-2. Identify the Causal Effect\n", "We say that Treatment causes Outcome if changing Treatment leads to a change in Outcome keeping everything else constant.\n", "Thus in this step, by using properties of the causal graph, we identify the causal effect to be estimated" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#Identify the causal effect\n", "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step-3. Estimate the identified estimand" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.propensity_score_weighting\",target_units=\"ate\")\n", "# ATE = Average Treatment Effect\n", "# ATT = Average Treatment Effect on Treated (i.e. those who were assigned a different room)\n", "# ATC = Average Treatment Effect on Control (i.e. those who were not assigned a different room)\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is surprising. It means that having a different room assigned _decreases_ the chances of a cancellation. There's more to unpack here: is this the correct causal effect? Could it be that different rooms are assigned only when the booked room is unavailable, and therefore assigning a different room has a positive effect on the customer (as opposed to not assigning a room)?\n", "\n", "There could also be other mechanisms at play. Perhaps assigning a different room only happens at check-in, and the chances of a cancellation once the customer is already at the hotel are low? In that case, the graph is missing a critical variable on _when_ these events happen. Does `different_room_assigned` happen mostly on the day of the booking? Knowing that variable can help improve the graph and our analysis. \n", "\n", "While the associational analysis earlier indicated a positive correlation between `is_canceled` and `different_room_assigned`, estimating the causal effect using DoWhy presents a different picture. It implies that a decision/policy to reduce the number of `different_room_assigned` at hotels may be counter-productive.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step-4. Refute results\n", "\n", "Note that the causal part does not come from data. It comes from your *assumptions* that lead to *identification*. Data is simply used for statistical *estimation*. Thus it becomes critical to verify whether our assumptions were even correct in the first step or not!\n", "\n", "What happens when another common cause exists?\n", "What happens when the treatment itself was placebo?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Method-1\n", "**Random Common Cause:-** *Adds randomly drawn covariates to data and re-runs the analysis to see if the causal estimate changes or not. If our assumption was originally correct then the causal estimate shouldn't change by much.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute1_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"random_common_cause\")\n", "print(refute1_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Method-2\n", "**Placebo Treatment Refuter:-** *Randomly assigns any covariate as a treatment and re-runs the analysis. If our assumptions were correct then this newly found out estimate should go to 0.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute2_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\")\n", "print(refute2_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Method-3\n", "**Data Subset Refuter:-** *Creates subsets of the data(similar to cross-validation) and checks whether the causal estimates vary across subsets. If our assumptions were correct there shouldn't be much variation.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute3_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\")\n", "print(refute3_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that our estimate passes all three refutation tests. This does not prove its correctness, but it increases confidence in the estimate. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.12" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exploring Causes of Hotel Booking Cancellations" ] }, { "attachments": { "Screenshot%20from%202020-09-29%2019-08-50.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "We consider what factors cause a hotel booking to be cancelled. This analysis is based on a hotel bookings dataset from [Antonio, Almeida and Nunes (2019)](https://www.sciencedirect.com/science/article/pii/S2352340918315191). On GitHub, the dataset is available at [rfordatascience/tidytuesday](https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-02-11/readme.md). \n", "\n", "There can be different reasons for why a booking is cancelled. A customer may have requested something that was not available (e.g., car parking), a customer may have found later that the hotel did not meet their requirements, or a customer may have simply cancelled their entire trip. Some of these like car parking are actionable by the hotel whereas others like trip cancellation are outside the hotel's control. In any case, we would like to better understand which of these factors cause booking cancellations. \n", "\n", "The gold standard of finding this out would be to use experiments such as *Randomized Controlled Trials* wherein each customer is randomly assigned to one of the two categories i.e. each customer is either assigned a car parking or not. However, such an experiment can be too costly and also unethical in some cases (for example, a hotel would start losing its reputation if people learn that its randomly assigning people to different level of service). \n", "\n", "Can we somehow answer our query using only observational data or data that has been collected in the past?\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import dowhy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Description\n", "For a quick glance of the features and their descriptions the reader is referred here.\n", "https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-02-11/readme.md" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = pd.read_csv('https://raw.githubusercontent.com/Sid-darthvader/DoWhy-The-Causal-Story-Behind-Hotel-Booking-Cancellations/master/hotel_bookings.csv')\n", "dataset.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Feature Engineering\n", "\n", "Lets create some new and meaningful features so as to reduce the dimensionality of the dataset. \n", "- **Total Stay** = stays_in_weekend_nights + stays_in_week_nights\n", "- **Guests** = adults + children + babies\n", "- **Different_room_assigned** = 1 if reserved_room_type & assigned_room_type are different, 0 otherwise." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Total stay in nights\n", "dataset['total_stay'] = dataset['stays_in_week_nights']+dataset['stays_in_weekend_nights']\n", "# Total number of guests\n", "dataset['guests'] = dataset['adults']+dataset['children'] +dataset['babies']\n", "# Creating the different_room_assigned feature\n", "dataset['different_room_assigned']=0\n", "slice_indices =dataset['reserved_room_type']!=dataset['assigned_room_type']\n", "dataset.loc[slice_indices,'different_room_assigned']=1\n", "# Deleting older features\n", "dataset = dataset.drop(['stays_in_week_nights','stays_in_weekend_nights','adults','children','babies'\n", " ,'reserved_room_type','assigned_room_type'],axis=1)\n", "dataset.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also remove other columns that either contain NULL values or have too many unique values (e.g., agent ID). We also impute missing values of the `country` column with the most frequent country. We remove `distribution_channel` since it has a high overlap with `market_segment`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset.isnull().sum() # Country,Agent,Company contain 488,16340,112593 missing entries \n", "dataset = dataset.drop(['agent','company'],axis=1)\n", "# Replacing missing countries with most freqently occuring countries\n", "dataset['country']= dataset['country'].fillna(dataset['country'].mode()[0])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = dataset.drop(['reservation_status','reservation_status_date','arrival_date_day_of_month'],axis=1)\n", "dataset = dataset.drop(['arrival_date_year'],axis=1)\n", "dataset = dataset.drop(['distribution_channel'], axis=1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Replacing 1 by True and 0 by False for the experiment and outcome variables\n", "dataset['different_room_assigned']= dataset['different_room_assigned'].replace(1,True)\n", "dataset['different_room_assigned']= dataset['different_room_assigned'].replace(0,False)\n", "dataset['is_canceled']= dataset['is_canceled'].replace(1,True)\n", "dataset['is_canceled']= dataset['is_canceled'].replace(0,False)\n", "dataset.dropna(inplace=True)\n", "print(dataset.columns)\n", "dataset.iloc[:, 5:20].head(100)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = dataset[dataset.deposit_type==\"No Deposit\"]\n", "dataset.groupby(['deposit_type','is_canceled']).count()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset_copy = dataset.copy(deep=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating Expected Counts\n", "Since the number of number of cancellations and the number of times a different room was assigned is heavily imbalanced, we first choose 1000 observations at random to see that in how many cases do the variables; *'is_cancelled'* & *'different_room_assigned'* attain the same values. This whole process is then repeated 10000 times and the expected count turns out to be near 50% (i.e. the probability of these two variables attaining the same value at random).\n", "So statistically speaking, we have no definite conclusion at this stage. Thus assigning rooms different to what a customer had reserved during his booking earlier, may or may not lead to him/her cancelling that booking." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset.sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now consider the scenario when there were no booking changes and recalculate the expected count." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Expected Count when there are no booking changes \n", "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset[dataset[\"booking_changes\"]==0].sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the 2nd case, we take the scenario when there were booking changes(>0) and recalculate the expected count." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Expected Count when there are booking changes = 66.4%\n", "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset[dataset[\"booking_changes\"]>0].sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is definitely some change happening when the number of booking changes are non-zero. So it gives us a hint that *Booking Changes* may be affecting room cancellation.\n", "\n", "But is *Booking Changes* the only confounding variable? What if there were some unobserved confounders, regarding which we have no information(feature) present in our dataset. Would we still be able to make the same claims as before?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using DoWhy to estimate the causal effect" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step-1. Create a Causal Graph\n", "Represent your prior knowledge about the predictive modelling problem as a CI graph using assumptions. Don't worry, you need not specify the full graph at this stage. Even a partial graph would be enough and the rest can be figured out by *DoWhy* ;-)\n", "\n", "Here are a list of assumptions that have then been translated into a Causal Diagram:-\n", "\n", "- *Market Segment* has 2 levels, “TA” refers to the “Travel Agents” and “TO” means “Tour Operators” so it should affect the Lead Time (which is simply the number of days between booking and arrival).\n", "- *Country* would also play a role in deciding whether a person books early or not (hence more *Lead Time*) and what type of *Meal* a person would prefer.\n", "- *Lead Time* would definitely affected the number of *Days in Waitlist* (There are lesser chances of finding a reservation if you’re booking late). Additionally, higher *Lead Times* can also lead to *Cancellations*.\n", "- The number of *Days in Waitlist*, the *Total Stay* in nights and the number of *Guests* might affect whether the booking is cancelled or retained.\n", "- *Previous Booking Retentions* would affect whether a customer is a or not. Additionally, both of these variables would affect whether the booking get *cancelled* or not (Ex- A customer who has retained his past 5 bookings in the past has a higher chance of retaining this one also. Similarly a person who has been cancelling this booking has a higher chance of repeating the same).\n", "- *Booking Changes* would affect whether the customer is assigned a *different room* or not which might also lead to *cancellation*.\n", "- Finally, the number of *Booking Changes* being the only variable affecting *Treatment* and *Outcome* is highly unlikely and its possible that there might be some *Unobsevered Confounders*, regarding which we have no information being captured in our data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pygraphviz\n", "causal_graph = \"\"\"digraph {\n", "different_room_assigned[label=\"Different Room Assigned\"];\n", "is_canceled[label=\"Booking Cancelled\"];\n", "booking_changes[label=\"Booking Changes\"];\n", "previous_bookings_not_canceled[label=\"Previous Booking Retentions\"];\n", "days_in_waiting_list[label=\"Days in Waitlist\"];\n", "lead_time[label=\"Lead Time\"];\n", "market_segment[label=\"Market Segment\"];\n", "country[label=\"Country\"];\n", "U[label=\"Unobserved Confounders\",observed=\"no\"];\n", "is_repeated_guest;\n", "total_stay;\n", "guests;\n", "meal;\n", "hotel;\n", "U->{different_room_assigned,required_car_parking_spaces,guests,total_stay,total_of_special_requests};\n", "market_segment -> lead_time;\n", "lead_time->is_canceled; country -> lead_time;\n", "different_room_assigned -> is_canceled;\n", "country->meal;\n", "lead_time -> days_in_waiting_list;\n", "days_in_waiting_list ->{is_canceled,different_room_assigned};\n", "previous_bookings_not_canceled -> is_canceled;\n", "previous_bookings_not_canceled -> is_repeated_guest;\n", "is_repeated_guest -> {different_room_assigned,is_canceled};\n", "total_stay -> is_canceled;\n", "guests -> is_canceled;\n", "booking_changes -> different_room_assigned; booking_changes -> is_canceled; \n", "hotel -> {different_room_assigned,is_canceled};\n", "required_car_parking_spaces -> is_canceled;\n", "total_of_special_requests -> {booking_changes,is_canceled};\n", "country->{hotel, required_car_parking_spaces,total_of_special_requests};\n", "market_segment->{hotel, required_car_parking_spaces,total_of_special_requests};\n", "}\"\"\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the *Treatment* is assigning the same type of room reserved by the customer during Booking. *Outcome* would be whether the booking was cancelled or not.\n", "*Common Causes* represent the variables that according to us have a causal affect on both *Outcome* and *Treatment*.\n", "As per our causal assumptions, the 2 variables satisfying this criteria are *Booking Changes* and the *Unobserved Confounders*.\n", "So if we are not specifying the graph explicitly (Not Recommended!), one can also provide these as parameters in the function mentioned below.\n", "\n", "To aid in identification of causal effect, we remove the unobserved confounder node from the graph. (To check, you can use the original graph and run the following code. The `identify_effect` method will find that the effect cannot be identified.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model= dowhy.CausalModel(\n", " data = dataset,\n", " graph=causal_graph.replace(\"\\n\", \" \"),\n", " treatment=\"different_room_assigned\",\n", " outcome='is_canceled')\n", "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step-2. Identify the Causal Effect\n", "We say that Treatment causes Outcome if changing Treatment leads to a change in Outcome keeping everything else constant.\n", "Thus in this step, by using properties of the causal graph, we identify the causal effect to be estimated" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#Identify the causal effect\n", "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step-3. Estimate the identified estimand" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.propensity_score_weighting\",target_units=\"ate\")\n", "# ATE = Average Treatment Effect\n", "# ATT = Average Treatment Effect on Treated (i.e. those who were assigned a different room)\n", "# ATC = Average Treatment Effect on Control (i.e. those who were not assigned a different room)\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is surprising. It means that having a different room assigned _decreases_ the chances of a cancellation. There's more to unpack here: is this the correct causal effect? Could it be that different rooms are assigned only when the booked room is unavailable, and therefore assigning a different room has a positive effect on the customer (as opposed to not assigning a room)?\n", "\n", "There could also be other mechanisms at play. Perhaps assigning a different room only happens at check-in, and the chances of a cancellation once the customer is already at the hotel are low? In that case, the graph is missing a critical variable on _when_ these events happen. Does `different_room_assigned` happen mostly on the day of the booking? Knowing that variable can help improve the graph and our analysis. \n", "\n", "While the associational analysis earlier indicated a positive correlation between `is_canceled` and `different_room_assigned`, estimating the causal effect using DoWhy presents a different picture. It implies that a decision/policy to reduce the number of `different_room_assigned` at hotels may be counter-productive.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step-4. Refute results\n", "\n", "Note that the causal part does not come from data. It comes from your *assumptions* that lead to *identification*. Data is simply used for statistical *estimation*. Thus it becomes critical to verify whether our assumptions were even correct in the first step or not!\n", "\n", "What happens when another common cause exists?\n", "What happens when the treatment itself was placebo?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Method-1\n", "**Random Common Cause:-** *Adds randomly drawn covariates to data and re-runs the analysis to see if the causal estimate changes or not. If our assumption was originally correct then the causal estimate shouldn't change by much.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute1_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"random_common_cause\")\n", "print(refute1_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Method-2\n", "**Placebo Treatment Refuter:-** *Randomly assigns any covariate as a treatment and re-runs the analysis. If our assumptions were correct then this newly found out estimate should go to 0.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute2_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\")\n", "print(refute2_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Method-3\n", "**Data Subset Refuter:-** *Creates subsets of the data(similar to cross-validation) and checks whether the causal estimates vary across subsets. If our assumptions were correct there shouldn't be much variation.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute3_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\")\n", "print(refute3_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that our estimate passes all three refutation tests. This does not prove its correctness, but it increases confidence in the estimate. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.12" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 4 }

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Good thought on rewording the title here. To keep the focus on the application, how about "Exploring Causes of Hotel Booking Cancellations"

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/example_notebooks/DoWhy-The Causal Story Behind Hotel Booking Cancellations.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exploring Causes of Hotel Booking Cancellations" ] }, { "attachments": { "Screenshot%20from%202020-09-29%2019-08-50.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "We consider what factors cause a hotel booking to be cancelled. This analysis is based on a hotel bookings dataset from [Antonio, Almeida and Nunes (2019)](https://www.sciencedirect.com/science/article/pii/S2352340918315191). On GitHub, the dataset is available at [rfordatascience/tidytuesday](https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-02-11/readme.md). \n", "\n", "There can be different reasons for why a booking is cancelled. A customer may have requested something that was not available (e.g., car parking), a customer may have found later that the hotel did not meet their requirements, or a customer may have simply cancelled their entire trip. Some of these like car parking are actionable by the hotel whereas others like trip cancellation are outside the hotel's control. In any case, we would like to better understand which of these factors cause booking cancellations. \n", "\n", "The gold standard of finding this out would be to use experiments such as *Randomized Controlled Trials* wherein each customer is randomly assigned to one of the two categories i.e. each customer is either assigned a car parking or not. However, such an experiment can be too costly and also unethical in some cases (for example, a hotel would start losing its reputation if people learn that its randomly assigning people to different level of service). \n", "\n", "Can we somehow answer our query using only observational data or data that has been collected in the past?\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%reload_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Config dict to set the logging level\n", "import logging.config\n", "DEFAULT_LOGGING = {\n", " 'version': 1,\n", " 'disable_existing_loggers': False,\n", " 'loggers': {\n", " '': {\n", " 'level': 'INFO',\n", " },\n", " }\n", "}\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "# Disabling warnings output\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning, ConvergenceWarning\n", "warnings.filterwarnings(action='ignore', category=DataConversionWarning)\n", "warnings.filterwarnings(action='ignore', category=ConvergenceWarning)\n", "warnings.filterwarnings(action='ignore', category=UserWarning)\n", "\n", "#!pip install dowhy\n", "import dowhy\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Description\n", "For a quick glance of the features and their descriptions the reader is referred here.\n", "https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-02-11/readme.md" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = pd.read_csv('https://raw.githubusercontent.com/Sid-darthvader/DoWhy-The-Causal-Story-Behind-Hotel-Booking-Cancellations/master/hotel_bookings.csv')\n", "dataset.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Feature Engineering\n", "\n", "Lets create some new and meaningful features so as to reduce the dimensionality of the dataset. \n", "- **Total Stay** = stays_in_weekend_nights + stays_in_week_nights\n", "- **Guests** = adults + children + babies\n", "- **Different_room_assigned** = 1 if reserved_room_type & assigned_room_type are different, 0 otherwise." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Total stay in nights\n", "dataset['total_stay'] = dataset['stays_in_week_nights']+dataset['stays_in_weekend_nights']\n", "# Total number of guests\n", "dataset['guests'] = dataset['adults']+dataset['children'] +dataset['babies']\n", "# Creating the different_room_assigned feature\n", "dataset['different_room_assigned']=0\n", "slice_indices =dataset['reserved_room_type']!=dataset['assigned_room_type']\n", "dataset.loc[slice_indices,'different_room_assigned']=1\n", "# Deleting older features\n", "dataset = dataset.drop(['stays_in_week_nights','stays_in_weekend_nights','adults','children','babies'\n", " ,'reserved_room_type','assigned_room_type'],axis=1)\n", "dataset.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also remove other columns that either contain NULL values or have too many unique values (e.g., agent ID). We also impute missing values of the `country` column with the most frequent country. We remove `distribution_channel` since it has a high overlap with `market_segment`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset.isnull().sum() # Country,Agent,Company contain 488,16340,112593 missing entries \n", "dataset = dataset.drop(['agent','company'],axis=1)\n", "# Replacing missing countries with most freqently occuring countries\n", "dataset['country']= dataset['country'].fillna(dataset['country'].mode()[0])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = dataset.drop(['reservation_status','reservation_status_date','arrival_date_day_of_month'],axis=1)\n", "dataset = dataset.drop(['arrival_date_year'],axis=1)\n", "dataset = dataset.drop(['distribution_channel'], axis=1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Replacing 1 by True and 0 by False for the experiment and outcome variables\n", "dataset['different_room_assigned']= dataset['different_room_assigned'].replace(1,True)\n", "dataset['different_room_assigned']= dataset['different_room_assigned'].replace(0,False)\n", "dataset['is_canceled']= dataset['is_canceled'].replace(1,True)\n", "dataset['is_canceled']= dataset['is_canceled'].replace(0,False)\n", "dataset.dropna(inplace=True)\n", "print(dataset.columns)\n", "dataset.iloc[:, 5:20].head(100)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = dataset[dataset.deposit_type==\"No Deposit\"]\n", "dataset.groupby(['deposit_type','is_canceled']).count()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset_copy = dataset.copy(deep=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating Expected Counts\n", "Since the number of number of cancellations and the number of times a different room was assigned is heavily imbalanced, we first choose 1000 observations at random to see that in how many cases do the variables; *'is_cancelled'* & *'different_room_assigned'* attain the same values. This whole process is then repeated 10000 times and the expected count turns out to be near 50% (i.e. the probability of these two variables attaining the same value at random).\n", "So statistically speaking, we have no definite conclusion at this stage. Thus assigning rooms different to what a customer had reserved during his booking earlier, may or may not lead to him/her cancelling that booking." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset.sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now consider the scenario when there were no booking changes and recalculate the expected count." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Expected Count when there are no booking changes \n", "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset[dataset[\"booking_changes\"]==0].sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the 2nd case, we take the scenario when there were booking changes(>0) and recalculate the expected count." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Expected Count when there are booking changes = 66.4%\n", "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset[dataset[\"booking_changes\"]>0].sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is definitely some change happening when the number of booking changes are non-zero. So it gives us a hint that *Booking Changes* may be affecting room cancellation.\n", "\n", "But is *Booking Changes* the only confounding variable? What if there were some unobserved confounders, regarding which we have no information(feature) present in our dataset. Would we still be able to make the same claims as before?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using DoWhy to estimate the causal effect" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step-1. Create a Causal Graph\n", "Represent your prior knowledge about the predictive modelling problem as a CI graph using assumptions. Don't worry, you need not specify the full graph at this stage. Even a partial graph would be enough and the rest can be figured out by *DoWhy* ;-)\n", "\n", "Here are a list of assumptions that have then been translated into a Causal Diagram:-\n", "\n", "- *Market Segment* has 2 levels, “TA” refers to the “Travel Agents” and “TO” means “Tour Operators” so it should affect the Lead Time (which is simply the number of days between booking and arrival).\n", "- *Country* would also play a role in deciding whether a person books early or not (hence more *Lead Time*) and what type of *Meal* a person would prefer.\n", "- *Lead Time* would definitely affected the number of *Days in Waitlist* (There are lesser chances of finding a reservation if you’re booking late). Additionally, higher *Lead Times* can also lead to *Cancellations*.\n", "- The number of *Days in Waitlist*, the *Total Stay* in nights and the number of *Guests* might affect whether the booking is cancelled or retained.\n", "- *Previous Booking Retentions* would affect whether a customer is a or not. Additionally, both of these variables would affect whether the booking get *cancelled* or not (Ex- A customer who has retained his past 5 bookings in the past has a higher chance of retaining this one also. Similarly a person who has been cancelling this booking has a higher chance of repeating the same).\n", "- *Booking Changes* would affect whether the customer is assigned a *different room* or not which might also lead to *cancellation*.\n", "- Finally, the number of *Booking Changes* being the only variable affecting *Treatment* and *Outcome* is highly unlikely and its possible that there might be some *Unobsevered Confounders*, regarding which we have no information being captured in our data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pygraphviz\n", "causal_graph = \"\"\"digraph {\n", "different_room_assigned[label=\"Different Room Assigned\"];\n", "is_canceled[label=\"Booking Cancelled\"];\n", "booking_changes[label=\"Booking Changes\"];\n", "previous_bookings_not_canceled[label=\"Previous Booking Retentions\"];\n", "days_in_waiting_list[label=\"Days in Waitlist\"];\n", "lead_time[label=\"Lead Time\"];\n", "market_segment[label=\"Market Segment\"];\n", "country[label=\"Country\"];\n", "U[label=\"Unobserved Confounders\",observed=\"no\"];\n", "is_repeated_guest;\n", "total_stay;\n", "guests;\n", "meal;\n", "hotel;\n", "U->{different_room_assigned,required_car_parking_spaces,guests,total_stay,total_of_special_requests};\n", "market_segment -> lead_time;\n", "lead_time->is_canceled; country -> lead_time;\n", "different_room_assigned -> is_canceled;\n", "country->meal;\n", "lead_time -> days_in_waiting_list;\n", "days_in_waiting_list ->{is_canceled,different_room_assigned};\n", "previous_bookings_not_canceled -> is_canceled;\n", "previous_bookings_not_canceled -> is_repeated_guest;\n", "is_repeated_guest -> {different_room_assigned,is_canceled};\n", "total_stay -> is_canceled;\n", "guests -> is_canceled;\n", "booking_changes -> different_room_assigned; booking_changes -> is_canceled; \n", "hotel -> {different_room_assigned,is_canceled};\n", "required_car_parking_spaces -> is_canceled;\n", "total_of_special_requests -> {booking_changes,is_canceled};\n", "country->{hotel, required_car_parking_spaces,total_of_special_requests};\n", "market_segment->{hotel, required_car_parking_spaces,total_of_special_requests};\n", "}\"\"\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the *Treatment* is assigning the same type of room reserved by the customer during Booking. *Outcome* would be whether the booking was cancelled or not.\n", "*Common Causes* represent the variables that according to us have a causal affect on both *Outcome* and *Treatment*.\n", "As per our causal assumptions, the 2 variables satisfying this criteria are *Booking Changes* and the *Unobserved Confounders*.\n", "So if we are not specifying the graph explicitly (Not Recommended!), one can also provide these as parameters in the function mentioned below.\n", "\n", "To aid in identification of causal effect, we remove the unobserved confounder node from the graph. (To check, you can use the original graph and run the following code. The `identify_effect` method will find that the effect cannot be identified.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model= dowhy.CausalModel(\n", " data = dataset,\n", " graph=causal_graph.replace(\"\\n\", \" \"),\n", " treatment=\"different_room_assigned\",\n", " outcome='is_canceled')\n", "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step-2. Identify the Causal Effect\n", "We say that Treatment causes Outcome if changing Treatment leads to a change in Outcome keeping everything else constant.\n", "Thus in this step, by using properties of the causal graph, we identify the causal effect to be estimated" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#Identify the causal effect\n", "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step-3. Estimate the identified estimand" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.propensity_score_weighting\",target_units=\"ate\")\n", "# ATE = Average Treatment Effect\n", "# ATT = Average Treatment Effect on Treated (i.e. those who were assigned a different room)\n", "# ATC = Average Treatment Effect on Control (i.e. those who were not assigned a different room)\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is surprising. It means that having a different room assigned _decreases_ the chances of a cancellation. There's more to unpack here: is this the correct causal effect? Could it be that different rooms are assigned only when the booked room is unavailable, and therefore assigning a different room has a positive effect on the customer (as opposed to not assigning a room)?\n", "\n", "There could also be other mechanisms at play. Perhaps assigning a different room only happens at check-in, and the chances of a cancellation once the customer is already at the hotel are low? In that case, the graph is missing a critical variable on _when_ these events happen. Does `different_room_assigned` happen mostly on the day of the booking? Knowing that variable can help improve the graph and our analysis. \n", "\n", "While the associational analysis earlier indicated a positive correlation between `is_canceled` and `different_room_assigned`, estimating the causal effect using DoWhy presents a different picture. It implies that a decision/policy to reduce the number of `different_room_assigned` at hotels may be counter-productive.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step-4. Refute results\n", "\n", "Note that the causal part does not come from data. It comes from your *assumptions* that lead to *identification*. Data is simply used for statistical *estimation*. Thus it becomes critical to verify whether our assumptions were even correct in the first step or not!\n", "\n", "What happens when another common cause exists?\n", "What happens when the treatment itself was placebo?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Method-1\n", "**Random Common Cause:-** *Adds randomly drawn covariates to data and re-runs the analysis to see if the causal estimate changes or not. If our assumption was originally correct then the causal estimate shouldn't change by much.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute1_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"random_common_cause\")\n", "print(refute1_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Method-2\n", "**Placebo Treatment Refuter:-** *Randomly assigns any covariate as a treatment and re-runs the analysis. If our assumptions were correct then this newly found out estimate should go to 0.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute2_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\")\n", "print(refute2_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Method-3\n", "**Data Subset Refuter:-** *Creates subsets of the data(similar to cross-validation) and checks whether the causal estimates vary across subsets. If our assumptions were correct there shouldn't be much variation.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute3_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\")\n", "print(refute3_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that our estimate passes all three refutation tests. This does not prove its correctness, but it increases confidence in the estimate. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.12" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exploring Causes of Hotel Booking Cancellations" ] }, { "attachments": { "Screenshot%20from%202020-09-29%2019-08-50.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "We consider what factors cause a hotel booking to be cancelled. This analysis is based on a hotel bookings dataset from [Antonio, Almeida and Nunes (2019)](https://www.sciencedirect.com/science/article/pii/S2352340918315191). On GitHub, the dataset is available at [rfordatascience/tidytuesday](https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-02-11/readme.md). \n", "\n", "There can be different reasons for why a booking is cancelled. A customer may have requested something that was not available (e.g., car parking), a customer may have found later that the hotel did not meet their requirements, or a customer may have simply cancelled their entire trip. Some of these like car parking are actionable by the hotel whereas others like trip cancellation are outside the hotel's control. In any case, we would like to better understand which of these factors cause booking cancellations. \n", "\n", "The gold standard of finding this out would be to use experiments such as *Randomized Controlled Trials* wherein each customer is randomly assigned to one of the two categories i.e. each customer is either assigned a car parking or not. However, such an experiment can be too costly and also unethical in some cases (for example, a hotel would start losing its reputation if people learn that its randomly assigning people to different level of service). \n", "\n", "Can we somehow answer our query using only observational data or data that has been collected in the past?\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import dowhy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Description\n", "For a quick glance of the features and their descriptions the reader is referred here.\n", "https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-02-11/readme.md" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = pd.read_csv('https://raw.githubusercontent.com/Sid-darthvader/DoWhy-The-Causal-Story-Behind-Hotel-Booking-Cancellations/master/hotel_bookings.csv')\n", "dataset.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Feature Engineering\n", "\n", "Lets create some new and meaningful features so as to reduce the dimensionality of the dataset. \n", "- **Total Stay** = stays_in_weekend_nights + stays_in_week_nights\n", "- **Guests** = adults + children + babies\n", "- **Different_room_assigned** = 1 if reserved_room_type & assigned_room_type are different, 0 otherwise." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Total stay in nights\n", "dataset['total_stay'] = dataset['stays_in_week_nights']+dataset['stays_in_weekend_nights']\n", "# Total number of guests\n", "dataset['guests'] = dataset['adults']+dataset['children'] +dataset['babies']\n", "# Creating the different_room_assigned feature\n", "dataset['different_room_assigned']=0\n", "slice_indices =dataset['reserved_room_type']!=dataset['assigned_room_type']\n", "dataset.loc[slice_indices,'different_room_assigned']=1\n", "# Deleting older features\n", "dataset = dataset.drop(['stays_in_week_nights','stays_in_weekend_nights','adults','children','babies'\n", " ,'reserved_room_type','assigned_room_type'],axis=1)\n", "dataset.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also remove other columns that either contain NULL values or have too many unique values (e.g., agent ID). We also impute missing values of the `country` column with the most frequent country. We remove `distribution_channel` since it has a high overlap with `market_segment`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset.isnull().sum() # Country,Agent,Company contain 488,16340,112593 missing entries \n", "dataset = dataset.drop(['agent','company'],axis=1)\n", "# Replacing missing countries with most freqently occuring countries\n", "dataset['country']= dataset['country'].fillna(dataset['country'].mode()[0])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = dataset.drop(['reservation_status','reservation_status_date','arrival_date_day_of_month'],axis=1)\n", "dataset = dataset.drop(['arrival_date_year'],axis=1)\n", "dataset = dataset.drop(['distribution_channel'], axis=1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Replacing 1 by True and 0 by False for the experiment and outcome variables\n", "dataset['different_room_assigned']= dataset['different_room_assigned'].replace(1,True)\n", "dataset['different_room_assigned']= dataset['different_room_assigned'].replace(0,False)\n", "dataset['is_canceled']= dataset['is_canceled'].replace(1,True)\n", "dataset['is_canceled']= dataset['is_canceled'].replace(0,False)\n", "dataset.dropna(inplace=True)\n", "print(dataset.columns)\n", "dataset.iloc[:, 5:20].head(100)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset = dataset[dataset.deposit_type==\"No Deposit\"]\n", "dataset.groupby(['deposit_type','is_canceled']).count()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dataset_copy = dataset.copy(deep=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating Expected Counts\n", "Since the number of number of cancellations and the number of times a different room was assigned is heavily imbalanced, we first choose 1000 observations at random to see that in how many cases do the variables; *'is_cancelled'* & *'different_room_assigned'* attain the same values. This whole process is then repeated 10000 times and the expected count turns out to be near 50% (i.e. the probability of these two variables attaining the same value at random).\n", "So statistically speaking, we have no definite conclusion at this stage. Thus assigning rooms different to what a customer had reserved during his booking earlier, may or may not lead to him/her cancelling that booking." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset.sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now consider the scenario when there were no booking changes and recalculate the expected count." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Expected Count when there are no booking changes \n", "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset[dataset[\"booking_changes\"]==0].sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the 2nd case, we take the scenario when there were booking changes(>0) and recalculate the expected count." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Expected Count when there are booking changes = 66.4%\n", "counts_sum=0\n", "for i in range(1,10000):\n", " counts_i = 0\n", " rdf = dataset[dataset[\"booking_changes\"]>0].sample(1000)\n", " counts_i = rdf[rdf[\"is_canceled\"]== rdf[\"different_room_assigned\"]].shape[0]\n", " counts_sum+= counts_i\n", "counts_sum/10000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is definitely some change happening when the number of booking changes are non-zero. So it gives us a hint that *Booking Changes* may be affecting room cancellation.\n", "\n", "But is *Booking Changes* the only confounding variable? What if there were some unobserved confounders, regarding which we have no information(feature) present in our dataset. Would we still be able to make the same claims as before?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using DoWhy to estimate the causal effect" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step-1. Create a Causal Graph\n", "Represent your prior knowledge about the predictive modelling problem as a CI graph using assumptions. Don't worry, you need not specify the full graph at this stage. Even a partial graph would be enough and the rest can be figured out by *DoWhy* ;-)\n", "\n", "Here are a list of assumptions that have then been translated into a Causal Diagram:-\n", "\n", "- *Market Segment* has 2 levels, “TA” refers to the “Travel Agents” and “TO” means “Tour Operators” so it should affect the Lead Time (which is simply the number of days between booking and arrival).\n", "- *Country* would also play a role in deciding whether a person books early or not (hence more *Lead Time*) and what type of *Meal* a person would prefer.\n", "- *Lead Time* would definitely affected the number of *Days in Waitlist* (There are lesser chances of finding a reservation if you’re booking late). Additionally, higher *Lead Times* can also lead to *Cancellations*.\n", "- The number of *Days in Waitlist*, the *Total Stay* in nights and the number of *Guests* might affect whether the booking is cancelled or retained.\n", "- *Previous Booking Retentions* would affect whether a customer is a or not. Additionally, both of these variables would affect whether the booking get *cancelled* or not (Ex- A customer who has retained his past 5 bookings in the past has a higher chance of retaining this one also. Similarly a person who has been cancelling this booking has a higher chance of repeating the same).\n", "- *Booking Changes* would affect whether the customer is assigned a *different room* or not which might also lead to *cancellation*.\n", "- Finally, the number of *Booking Changes* being the only variable affecting *Treatment* and *Outcome* is highly unlikely and its possible that there might be some *Unobsevered Confounders*, regarding which we have no information being captured in our data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pygraphviz\n", "causal_graph = \"\"\"digraph {\n", "different_room_assigned[label=\"Different Room Assigned\"];\n", "is_canceled[label=\"Booking Cancelled\"];\n", "booking_changes[label=\"Booking Changes\"];\n", "previous_bookings_not_canceled[label=\"Previous Booking Retentions\"];\n", "days_in_waiting_list[label=\"Days in Waitlist\"];\n", "lead_time[label=\"Lead Time\"];\n", "market_segment[label=\"Market Segment\"];\n", "country[label=\"Country\"];\n", "U[label=\"Unobserved Confounders\",observed=\"no\"];\n", "is_repeated_guest;\n", "total_stay;\n", "guests;\n", "meal;\n", "hotel;\n", "U->{different_room_assigned,required_car_parking_spaces,guests,total_stay,total_of_special_requests};\n", "market_segment -> lead_time;\n", "lead_time->is_canceled; country -> lead_time;\n", "different_room_assigned -> is_canceled;\n", "country->meal;\n", "lead_time -> days_in_waiting_list;\n", "days_in_waiting_list ->{is_canceled,different_room_assigned};\n", "previous_bookings_not_canceled -> is_canceled;\n", "previous_bookings_not_canceled -> is_repeated_guest;\n", "is_repeated_guest -> {different_room_assigned,is_canceled};\n", "total_stay -> is_canceled;\n", "guests -> is_canceled;\n", "booking_changes -> different_room_assigned; booking_changes -> is_canceled; \n", "hotel -> {different_room_assigned,is_canceled};\n", "required_car_parking_spaces -> is_canceled;\n", "total_of_special_requests -> {booking_changes,is_canceled};\n", "country->{hotel, required_car_parking_spaces,total_of_special_requests};\n", "market_segment->{hotel, required_car_parking_spaces,total_of_special_requests};\n", "}\"\"\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the *Treatment* is assigning the same type of room reserved by the customer during Booking. *Outcome* would be whether the booking was cancelled or not.\n", "*Common Causes* represent the variables that according to us have a causal affect on both *Outcome* and *Treatment*.\n", "As per our causal assumptions, the 2 variables satisfying this criteria are *Booking Changes* and the *Unobserved Confounders*.\n", "So if we are not specifying the graph explicitly (Not Recommended!), one can also provide these as parameters in the function mentioned below.\n", "\n", "To aid in identification of causal effect, we remove the unobserved confounder node from the graph. (To check, you can use the original graph and run the following code. The `identify_effect` method will find that the effect cannot be identified.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model= dowhy.CausalModel(\n", " data = dataset,\n", " graph=causal_graph.replace(\"\\n\", \" \"),\n", " treatment=\"different_room_assigned\",\n", " outcome='is_canceled')\n", "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step-2. Identify the Causal Effect\n", "We say that Treatment causes Outcome if changing Treatment leads to a change in Outcome keeping everything else constant.\n", "Thus in this step, by using properties of the causal graph, we identify the causal effect to be estimated" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#Identify the causal effect\n", "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step-3. Estimate the identified estimand" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.propensity_score_weighting\",target_units=\"ate\")\n", "# ATE = Average Treatment Effect\n", "# ATT = Average Treatment Effect on Treated (i.e. those who were assigned a different room)\n", "# ATC = Average Treatment Effect on Control (i.e. those who were not assigned a different room)\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is surprising. It means that having a different room assigned _decreases_ the chances of a cancellation. There's more to unpack here: is this the correct causal effect? Could it be that different rooms are assigned only when the booked room is unavailable, and therefore assigning a different room has a positive effect on the customer (as opposed to not assigning a room)?\n", "\n", "There could also be other mechanisms at play. Perhaps assigning a different room only happens at check-in, and the chances of a cancellation once the customer is already at the hotel are low? In that case, the graph is missing a critical variable on _when_ these events happen. Does `different_room_assigned` happen mostly on the day of the booking? Knowing that variable can help improve the graph and our analysis. \n", "\n", "While the associational analysis earlier indicated a positive correlation between `is_canceled` and `different_room_assigned`, estimating the causal effect using DoWhy presents a different picture. It implies that a decision/policy to reduce the number of `different_room_assigned` at hotels may be counter-productive.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step-4. Refute results\n", "\n", "Note that the causal part does not come from data. It comes from your *assumptions* that lead to *identification*. Data is simply used for statistical *estimation*. Thus it becomes critical to verify whether our assumptions were even correct in the first step or not!\n", "\n", "What happens when another common cause exists?\n", "What happens when the treatment itself was placebo?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Method-1\n", "**Random Common Cause:-** *Adds randomly drawn covariates to data and re-runs the analysis to see if the causal estimate changes or not. If our assumption was originally correct then the causal estimate shouldn't change by much.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute1_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"random_common_cause\")\n", "print(refute1_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Method-2\n", "**Placebo Treatment Refuter:-** *Randomly assigns any covariate as a treatment and re-runs the analysis. If our assumptions were correct then this newly found out estimate should go to 0.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute2_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\")\n", "print(refute2_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Method-3\n", "**Data Subset Refuter:-** *Creates subsets of the data(similar to cross-validation) and checks whether the causal estimates vary across subsets. If our assumptions were correct there shouldn't be much variation.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "refute3_results=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\")\n", "print(refute3_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that our estimate passes all three refutation tests. This does not prove its correctness, but it increases confidence in the estimate. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.12" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 4 }

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Done

petergtz

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/example_notebooks/dowhy_simple_example.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Example for Calculating the Causal Effect\n", "This is a quick introduction to the DoWhy causal inference library.\n", "We will load in a sample dataset and estimate the causal effect of a (pre-specified) treatment variable on a (pre-specified) outcome variable.\n", "\n", "First, let us load all required packages." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "from dowhy import CausalModel\n", "import dowhy.datasets \n", "\n", "# Avoid printing dataconversion warnings from sklearn and numpy\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "warnings.filterwarnings(action='ignore', category=DataConversionWarning)\n", "warnings.filterwarnings(action='ignore', category=FutureWarning)\n", "\n", "# Config dict to set the logging level\n", "import logging\n", "import logging.config\n", "DEFAULT_LOGGING = {\n", " 'version': 1,\n", " 'disable_existing_loggers': False,\n", " 'loggers': {\n", " '': {\n", " 'level': 'WARN',\n", " },\n", " }\n", "}\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "logging.info(\"Getting started with DoWhy. Running notebook...\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us load a dataset. For simplicity, we simulate a dataset with linear relationships between common causes and treatment, and common causes and outcome. \n", "\n", "Beta is the true causal effect. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(beta=10,\n", " num_common_causes=5,\n", " num_instruments = 2,\n", " num_effect_modifiers=1,\n", " num_samples=5000, \n", " treatment_is_binary=True,\n", " stddev_treatment_noise=10,\n", " num_discrete_common_causes=1)\n", "df = data[\"df\"]\n", "print(df.head())\n", "print(data[\"dot_graph\"])\n", "print(\"\\n\")\n", "print(data[\"gml_graph\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we are using a pandas dataframe to load the data. At present, DoWhy only supports pandas dataframe as input." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 1 (recommended): Input causal graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now input a causal graph in the GML graph format (recommended). You can also use the DOT format.\n", "\n", "To create the causal graph for your dataset, you can use a tool like [DAGitty](http://dagitty.net/dags.html#) that provides a GUI to construct the graph. You can export the graph string that it generates. The graph string is very close to the DOT format: just rename `dag` to `digraph`, remove newlines and add a semicolon after every line, to convert it to the DOT format and input to DoWhy. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# With graph\n", "model=CausalModel(\n", " data = df,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=data[\"gml_graph\"]\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above causal graph shows the assumptions encoded in the causal model. We can now use this graph to first identify \n", "the causal effect (go from a causal estimand to a probability expression), and then estimate the causal effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DoWhy philosophy: Keep identification and estimation separate\n", "\n", "Identification can be achieved without access to the data, acccesing only the graph. This results in an expression to be computed. This expression can then be evaluated using the available data in the estimation step.\n", "It is important to understand that these are orthogonal steps.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the parameter flag *proceed\\_when\\_unidentifiable*. It needs to be set to *True* to convey the assumption that we are ignoring any unobserved confounding. The default behavior is to prompt the user to double-check that the unobserved confounders can be ignored. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "causal_estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\")\n", "print(causal_estimate)\n", "print(\"Causal Estimate is \" + str(causal_estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can input additional parameters to the estimate_effect method. For instance, to estimate the effect on any subset of the units, you can specify the \"target_units\" parameter which can be a string (\"ate\", \"att\", or \"atc\"), lambda function that filters rows of the data frame, or a new dataframe on which to compute the effect. You can also specify \"effect modifiers\" to estimate heterogeneous effects across these variables. See `help(CausalModel.estimate_effect)`. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Causal effect on the control group (ATC)\n", "causal_estimate_att = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\",\n", " target_units = \"atc\")\n", "print(causal_estimate_att)\n", "print(\"Causal Estimate is \" + str(causal_estimate_att.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 2: Specify common causes and instruments" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Without graph \n", "model= CausalModel( \n", " data=df, \n", " treatment=data[\"treatment_name\"], \n", " outcome=data[\"outcome_name\"], \n", " common_causes=data[\"common_causes_names\"],\n", " effect_modifiers=data[\"effect_modifier_names\"]) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get the same causal graph. Now identification and estimation is done as before.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\") \n", "print(estimate)\n", "print(\"Causal Estimate is \" + str(estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate\n", "\n", "Let us now look at ways of refuting the estimate obtained. Refutation methods provide tests that every correct estimator should pass. So if an estimator fails the refutation test (p-value is <0.05), then it means that there is some problem with the estimator. \n", "\n", "Note that we cannot verify that the estimate is correct, but we can reject it if it violates certain expected behavior (this is analogous to scientific theories that can be falsified but not proven true). The below refutation tests are based on either \n", " 1) **Invariant transformations**: changes in the data that should not change the estimate. Any estimator whose result varies significantly between the original data and the modified data fails the test; \n", " \n", " a) Random Common Cause\n", " \n", " b) Data Subset\n", " \n", " \n", " 2) **Nullifying transformations**: after the data change, the causal true estimate is zero. Any estimator whose result varies significantly from zero on the new data fails the test.\n", " \n", " a) Placebo Treatment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\", show_progress_bar=True)\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\", show_progress_bar=True, placebo_type=\"permute\")\n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the propensity score stratification estimator is reasonably robust to refutations.\n", "\n", "**Reproducability**: For reproducibility, you can add a parameter \"random_seed\" to any refutation method, as shown below.\n", "\n", "**Parallelization**: You can also use built-in parallelization to speed up the refutation process. Simply set `n_jobs` to a value greater than 1 to spread the workload to multiple CPUs, or set `n_jobs=-1` to use all CPUs. Currently, this is available only for `random_common_cause`, `placebo_treatment_refuter`, and `data_subset_refuter`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9, random_seed = 1, n_jobs=-1, verbose=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable\n", "\n", "This refutation does not return a p-value. Instead, it provides a _sensitivity_ test on how quickly the estimate changes if the identifying assumptions (used in `identify_effect`) are not valid. Specifically, it checks sensitivity to violation of the backdoor assumption: that all common causes are observed. \n", "\n", "To do so, it creates a new dataset with an additional common cause between treatment and outcome. To capture the effect of the common cause, the method takes as input the strength of common cause's effect on treatment and outcome. Based on these inputs on the common cause's effects, it changes the treatment and outcome values and then reruns the estimator. The hope is that the new estimate does not change drastically with a small effect of the unobserved common cause, indicating a robustness to any unobserved confounding.\n", "\n", "Another equivalent way of interpreting this procedure is to assume that there was already unobserved confounding present in the input data. The change in treatment and outcome values _removes_ the effect of whatever unobserved common cause was present in the original data. Then rerunning the estimator on this modified data provides the correct identified estimate and we hope that the difference between the new estimate and the original estimate is not too high, for some bounded value of the unobserved common cause's effect.\n", "\n", "**Importance of domain knowledge**: This test requires _domain knowledge_ to set plausible input values of the effect of unobserved confounding. We first show the result for a single value of confounder's effect on treatment and outcome." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is often more useful to inspect the trend as the effect of unobserved confounding is increased. For that, we can provide an array of hypothesized confounders' effects. The output is the *(min, max)* range of the estimated effects under different unobserved confounding." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=np.array([0.001, 0.005, 0.01, 0.02]), effect_strength_on_outcome=0.01)\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above plot shows how the estimate decreases as the hypothesized confounding on treatment increases. By domain knowledge, we may know the maximum plausible confounding effect on treatment. Since we see that the effect does not go beyond zero, we can safely conclude that the causal effect of treatment `v0` is positive.\n", "\n", "We can also vary the confounding effect on both treatment and outcome. We obtain a heatmap." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=[0.001, 0.005, 0.01, 0.02], \n", " effect_strength_on_outcome=[0.001, 0.005, 0.01,0.02])\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Automatically inferring effect strength parameters.** Finally, DoWhy supports automatic selection of the effect strength parameters. This is based on an assumption that the effect of the unobserved confounder on treatment or outcome cannot be stronger than that of any observed confounder. That is, we have collected data at least for the most relevant confounder. If that is the case, then we can bound the range of `effect_strength_on_treatment` and `effect_strength_on_outcome` by the effect strength of observed confounders. There is an additional optional parameter signifying whether the effect strength of unobserved confounder should be as high as the highest observed, or a fraction of it. You can set it using the optional `effect_fraction_on_treatment` and `effect_fraction_on_outcome` parameters. By default, these two parameters are 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_auto = model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\")\n", "print(res_unobserved_auto)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**: Assuming that the unobserved confounder does not affect the treatment or outcome more strongly than any observed confounder, the causal effect can be concluded to be positive." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Example for Calculating the Causal Effect\n", "This is a quick introduction to the DoWhy causal inference library.\n", "We will load in a sample dataset and estimate the causal effect of a (pre-specified) treatment variable on a (pre-specified) outcome variable.\n", "\n", "First, let us load all required packages." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "from dowhy import CausalModel\n", "import dowhy.datasets " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us load a dataset. For simplicity, we simulate a dataset with linear relationships between common causes and treatment, and common causes and outcome. \n", "\n", "Beta is the true causal effect. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(beta=10,\n", " num_common_causes=5,\n", " num_instruments = 2,\n", " num_effect_modifiers=1,\n", " num_samples=5000, \n", " treatment_is_binary=True,\n", " stddev_treatment_noise=10,\n", " num_discrete_common_causes=1)\n", "df = data[\"df\"]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we are using a pandas dataframe to load the data. At present, DoWhy only supports pandas dataframe as input." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 1 (recommended): Input causal graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now input a causal graph in the GML graph format (recommended). You can also use the DOT format.\n", "\n", "To create the causal graph for your dataset, you can use a tool like [DAGitty](http://dagitty.net/dags.html#) that provides a GUI to construct the graph. You can export the graph string that it generates. The graph string is very close to the DOT format: just rename `dag` to `digraph`, remove newlines and add a semicolon after every line, to convert it to the DOT format and input to DoWhy. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# With graph\n", "model=CausalModel(\n", " data = df,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=data[\"gml_graph\"]\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above causal graph shows the assumptions encoded in the causal model. We can now use this graph to first identify \n", "the causal effect (go from a causal estimand to a probability expression), and then estimate the causal effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DoWhy philosophy: Keep identification and estimation separate\n", "\n", "Identification can be achieved without access to the data, acccesing only the graph. This results in an expression to be computed. This expression can then be evaluated using the available data in the estimation step.\n", "It is important to understand that these are orthogonal steps.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the parameter flag *proceed\\_when\\_unidentifiable*. It needs to be set to *True* to convey the assumption that we are ignoring any unobserved confounding. The default behavior is to prompt the user to double-check that the unobserved confounders can be ignored. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "causal_estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\")\n", "print(causal_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can input additional parameters to the estimate_effect method. For instance, to estimate the effect on any subset of the units, you can specify the \"target_units\" parameter which can be a string (\"ate\", \"att\", or \"atc\"), lambda function that filters rows of the data frame, or a new dataframe on which to compute the effect. You can also specify \"effect modifiers\" to estimate heterogeneous effects across these variables. See `help(CausalModel.estimate_effect)`. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Causal effect on the control group (ATC)\n", "causal_estimate_att = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\",\n", " target_units = \"atc\")\n", "print(causal_estimate_att)\n", "print(\"Causal Estimate is \" + str(causal_estimate_att.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 2: Specify common causes and instruments" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Without graph \n", "model= CausalModel( \n", " data=df, \n", " treatment=data[\"treatment_name\"], \n", " outcome=data[\"outcome_name\"], \n", " common_causes=data[\"common_causes_names\"],\n", " effect_modifiers=data[\"effect_modifier_names\"]) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get the same causal graph. Now identification and estimation is done as before.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\") \n", "print(estimate)\n", "print(\"Causal Estimate is \" + str(estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate\n", "\n", "Let us now look at ways of refuting the estimate obtained. Refutation methods provide tests that every correct estimator should pass. So if an estimator fails the refutation test (p-value is <0.05), then it means that there is some problem with the estimator. \n", "\n", "Note that we cannot verify that the estimate is correct, but we can reject it if it violates certain expected behavior (this is analogous to scientific theories that can be falsified but not proven true). The below refutation tests are based on either \n", " 1) **Invariant transformations**: changes in the data that should not change the estimate. Any estimator whose result varies significantly between the original data and the modified data fails the test; \n", " \n", " a) Random Common Cause\n", " \n", " b) Data Subset\n", " \n", " \n", " 2) **Nullifying transformations**: after the data change, the causal true estimate is zero. Any estimator whose result varies significantly from zero on the new data fails the test.\n", " \n", " a) Placebo Treatment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\", show_progress_bar=True)\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\", show_progress_bar=True, placebo_type=\"permute\")\n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the propensity score stratification estimator is reasonably robust to refutations.\n", "\n", "**Reproducability**: For reproducibility, you can add a parameter \"random_seed\" to any refutation method, as shown below.\n", "\n", "**Parallelization**: You can also use built-in parallelization to speed up the refutation process. Simply set `n_jobs` to a value greater than 1 to spread the workload to multiple CPUs, or set `n_jobs=-1` to use all CPUs. Currently, this is available only for `random_common_cause`, `placebo_treatment_refuter`, and `data_subset_refuter`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9, random_seed = 1, n_jobs=-1, verbose=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable\n", "\n", "This refutation does not return a p-value. Instead, it provides a _sensitivity_ test on how quickly the estimate changes if the identifying assumptions (used in `identify_effect`) are not valid. Specifically, it checks sensitivity to violation of the backdoor assumption: that all common causes are observed. \n", "\n", "To do so, it creates a new dataset with an additional common cause between treatment and outcome. To capture the effect of the common cause, the method takes as input the strength of common cause's effect on treatment and outcome. Based on these inputs on the common cause's effects, it changes the treatment and outcome values and then reruns the estimator. The hope is that the new estimate does not change drastically with a small effect of the unobserved common cause, indicating a robustness to any unobserved confounding.\n", "\n", "Another equivalent way of interpreting this procedure is to assume that there was already unobserved confounding present in the input data. The change in treatment and outcome values _removes_ the effect of whatever unobserved common cause was present in the original data. Then rerunning the estimator on this modified data provides the correct identified estimate and we hope that the difference between the new estimate and the original estimate is not too high, for some bounded value of the unobserved common cause's effect.\n", "\n", "**Importance of domain knowledge**: This test requires _domain knowledge_ to set plausible input values of the effect of unobserved confounding. We first show the result for a single value of confounder's effect on treatment and outcome." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is often more useful to inspect the trend as the effect of unobserved confounding is increased. For that, we can provide an array of hypothesized confounders' effects. The output is the *(min, max)* range of the estimated effects under different unobserved confounding." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=np.array([0.001, 0.005, 0.01, 0.02]), effect_strength_on_outcome=0.01)\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above plot shows how the estimate decreases as the hypothesized confounding on treatment increases. By domain knowledge, we may know the maximum plausible confounding effect on treatment. Since we see that the effect does not go beyond zero, we can safely conclude that the causal effect of treatment `v0` is positive.\n", "\n", "We can also vary the confounding effect on both treatment and outcome. We obtain a heatmap." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=[0.001, 0.005, 0.01, 0.02], \n", " effect_strength_on_outcome=[0.001, 0.005, 0.01,0.02])\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Automatically inferring effect strength parameters.** Finally, DoWhy supports automatic selection of the effect strength parameters. This is based on an assumption that the effect of the unobserved confounder on treatment or outcome cannot be stronger than that of any observed confounder. That is, we have collected data at least for the most relevant confounder. If that is the case, then we can bound the range of `effect_strength_on_treatment` and `effect_strength_on_outcome` by the effect strength of observed confounders. There is an additional optional parameter signifying whether the effect strength of unobserved confounder should be as high as the highest observed, or a fraction of it. You can set it using the optional `effect_fraction_on_treatment` and `effect_fraction_on_outcome` parameters. By default, these two parameters are 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_auto = model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\")\n", "print(res_unobserved_auto)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**: Assuming that the unobserved confounder does not affect the treatment or outcome more strongly than any observed confounder, the causal effect can be concluded to be positive." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

we could just say, "Causal Effect".

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/example_notebooks/dowhy_simple_example.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Example for Calculating the Causal Effect\n", "This is a quick introduction to the DoWhy causal inference library.\n", "We will load in a sample dataset and estimate the causal effect of a (pre-specified) treatment variable on a (pre-specified) outcome variable.\n", "\n", "First, let us load all required packages." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "from dowhy import CausalModel\n", "import dowhy.datasets \n", "\n", "# Avoid printing dataconversion warnings from sklearn and numpy\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "warnings.filterwarnings(action='ignore', category=DataConversionWarning)\n", "warnings.filterwarnings(action='ignore', category=FutureWarning)\n", "\n", "# Config dict to set the logging level\n", "import logging\n", "import logging.config\n", "DEFAULT_LOGGING = {\n", " 'version': 1,\n", " 'disable_existing_loggers': False,\n", " 'loggers': {\n", " '': {\n", " 'level': 'WARN',\n", " },\n", " }\n", "}\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "logging.info(\"Getting started with DoWhy. Running notebook...\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us load a dataset. For simplicity, we simulate a dataset with linear relationships between common causes and treatment, and common causes and outcome. \n", "\n", "Beta is the true causal effect. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(beta=10,\n", " num_common_causes=5,\n", " num_instruments = 2,\n", " num_effect_modifiers=1,\n", " num_samples=5000, \n", " treatment_is_binary=True,\n", " stddev_treatment_noise=10,\n", " num_discrete_common_causes=1)\n", "df = data[\"df\"]\n", "print(df.head())\n", "print(data[\"dot_graph\"])\n", "print(\"\\n\")\n", "print(data[\"gml_graph\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we are using a pandas dataframe to load the data. At present, DoWhy only supports pandas dataframe as input." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 1 (recommended): Input causal graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now input a causal graph in the GML graph format (recommended). You can also use the DOT format.\n", "\n", "To create the causal graph for your dataset, you can use a tool like [DAGitty](http://dagitty.net/dags.html#) that provides a GUI to construct the graph. You can export the graph string that it generates. The graph string is very close to the DOT format: just rename `dag` to `digraph`, remove newlines and add a semicolon after every line, to convert it to the DOT format and input to DoWhy. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# With graph\n", "model=CausalModel(\n", " data = df,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=data[\"gml_graph\"]\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above causal graph shows the assumptions encoded in the causal model. We can now use this graph to first identify \n", "the causal effect (go from a causal estimand to a probability expression), and then estimate the causal effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DoWhy philosophy: Keep identification and estimation separate\n", "\n", "Identification can be achieved without access to the data, acccesing only the graph. This results in an expression to be computed. This expression can then be evaluated using the available data in the estimation step.\n", "It is important to understand that these are orthogonal steps.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the parameter flag *proceed\\_when\\_unidentifiable*. It needs to be set to *True* to convey the assumption that we are ignoring any unobserved confounding. The default behavior is to prompt the user to double-check that the unobserved confounders can be ignored. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "causal_estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\")\n", "print(causal_estimate)\n", "print(\"Causal Estimate is \" + str(causal_estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can input additional parameters to the estimate_effect method. For instance, to estimate the effect on any subset of the units, you can specify the \"target_units\" parameter which can be a string (\"ate\", \"att\", or \"atc\"), lambda function that filters rows of the data frame, or a new dataframe on which to compute the effect. You can also specify \"effect modifiers\" to estimate heterogeneous effects across these variables. See `help(CausalModel.estimate_effect)`. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Causal effect on the control group (ATC)\n", "causal_estimate_att = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\",\n", " target_units = \"atc\")\n", "print(causal_estimate_att)\n", "print(\"Causal Estimate is \" + str(causal_estimate_att.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 2: Specify common causes and instruments" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Without graph \n", "model= CausalModel( \n", " data=df, \n", " treatment=data[\"treatment_name\"], \n", " outcome=data[\"outcome_name\"], \n", " common_causes=data[\"common_causes_names\"],\n", " effect_modifiers=data[\"effect_modifier_names\"]) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get the same causal graph. Now identification and estimation is done as before.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\") \n", "print(estimate)\n", "print(\"Causal Estimate is \" + str(estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate\n", "\n", "Let us now look at ways of refuting the estimate obtained. Refutation methods provide tests that every correct estimator should pass. So if an estimator fails the refutation test (p-value is <0.05), then it means that there is some problem with the estimator. \n", "\n", "Note that we cannot verify that the estimate is correct, but we can reject it if it violates certain expected behavior (this is analogous to scientific theories that can be falsified but not proven true). The below refutation tests are based on either \n", " 1) **Invariant transformations**: changes in the data that should not change the estimate. Any estimator whose result varies significantly between the original data and the modified data fails the test; \n", " \n", " a) Random Common Cause\n", " \n", " b) Data Subset\n", " \n", " \n", " 2) **Nullifying transformations**: after the data change, the causal true estimate is zero. Any estimator whose result varies significantly from zero on the new data fails the test.\n", " \n", " a) Placebo Treatment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\", show_progress_bar=True)\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\", show_progress_bar=True, placebo_type=\"permute\")\n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the propensity score stratification estimator is reasonably robust to refutations.\n", "\n", "**Reproducability**: For reproducibility, you can add a parameter \"random_seed\" to any refutation method, as shown below.\n", "\n", "**Parallelization**: You can also use built-in parallelization to speed up the refutation process. Simply set `n_jobs` to a value greater than 1 to spread the workload to multiple CPUs, or set `n_jobs=-1` to use all CPUs. Currently, this is available only for `random_common_cause`, `placebo_treatment_refuter`, and `data_subset_refuter`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9, random_seed = 1, n_jobs=-1, verbose=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable\n", "\n", "This refutation does not return a p-value. Instead, it provides a _sensitivity_ test on how quickly the estimate changes if the identifying assumptions (used in `identify_effect`) are not valid. Specifically, it checks sensitivity to violation of the backdoor assumption: that all common causes are observed. \n", "\n", "To do so, it creates a new dataset with an additional common cause between treatment and outcome. To capture the effect of the common cause, the method takes as input the strength of common cause's effect on treatment and outcome. Based on these inputs on the common cause's effects, it changes the treatment and outcome values and then reruns the estimator. The hope is that the new estimate does not change drastically with a small effect of the unobserved common cause, indicating a robustness to any unobserved confounding.\n", "\n", "Another equivalent way of interpreting this procedure is to assume that there was already unobserved confounding present in the input data. The change in treatment and outcome values _removes_ the effect of whatever unobserved common cause was present in the original data. Then rerunning the estimator on this modified data provides the correct identified estimate and we hope that the difference between the new estimate and the original estimate is not too high, for some bounded value of the unobserved common cause's effect.\n", "\n", "**Importance of domain knowledge**: This test requires _domain knowledge_ to set plausible input values of the effect of unobserved confounding. We first show the result for a single value of confounder's effect on treatment and outcome." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is often more useful to inspect the trend as the effect of unobserved confounding is increased. For that, we can provide an array of hypothesized confounders' effects. The output is the *(min, max)* range of the estimated effects under different unobserved confounding." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=np.array([0.001, 0.005, 0.01, 0.02]), effect_strength_on_outcome=0.01)\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above plot shows how the estimate decreases as the hypothesized confounding on treatment increases. By domain knowledge, we may know the maximum plausible confounding effect on treatment. Since we see that the effect does not go beyond zero, we can safely conclude that the causal effect of treatment `v0` is positive.\n", "\n", "We can also vary the confounding effect on both treatment and outcome. We obtain a heatmap." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=[0.001, 0.005, 0.01, 0.02], \n", " effect_strength_on_outcome=[0.001, 0.005, 0.01,0.02])\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Automatically inferring effect strength parameters.** Finally, DoWhy supports automatic selection of the effect strength parameters. This is based on an assumption that the effect of the unobserved confounder on treatment or outcome cannot be stronger than that of any observed confounder. That is, we have collected data at least for the most relevant confounder. If that is the case, then we can bound the range of `effect_strength_on_treatment` and `effect_strength_on_outcome` by the effect strength of observed confounders. There is an additional optional parameter signifying whether the effect strength of unobserved confounder should be as high as the highest observed, or a fraction of it. You can set it using the optional `effect_fraction_on_treatment` and `effect_fraction_on_outcome` parameters. By default, these two parameters are 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_auto = model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\")\n", "print(res_unobserved_auto)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**: Assuming that the unobserved confounder does not affect the treatment or outcome more strongly than any observed confounder, the causal effect can be concluded to be positive." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Example for Calculating the Causal Effect\n", "This is a quick introduction to the DoWhy causal inference library.\n", "We will load in a sample dataset and estimate the causal effect of a (pre-specified) treatment variable on a (pre-specified) outcome variable.\n", "\n", "First, let us load all required packages." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "from dowhy import CausalModel\n", "import dowhy.datasets " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us load a dataset. For simplicity, we simulate a dataset with linear relationships between common causes and treatment, and common causes and outcome. \n", "\n", "Beta is the true causal effect. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(beta=10,\n", " num_common_causes=5,\n", " num_instruments = 2,\n", " num_effect_modifiers=1,\n", " num_samples=5000, \n", " treatment_is_binary=True,\n", " stddev_treatment_noise=10,\n", " num_discrete_common_causes=1)\n", "df = data[\"df\"]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we are using a pandas dataframe to load the data. At present, DoWhy only supports pandas dataframe as input." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 1 (recommended): Input causal graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now input a causal graph in the GML graph format (recommended). You can also use the DOT format.\n", "\n", "To create the causal graph for your dataset, you can use a tool like [DAGitty](http://dagitty.net/dags.html#) that provides a GUI to construct the graph. You can export the graph string that it generates. The graph string is very close to the DOT format: just rename `dag` to `digraph`, remove newlines and add a semicolon after every line, to convert it to the DOT format and input to DoWhy. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# With graph\n", "model=CausalModel(\n", " data = df,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=data[\"gml_graph\"]\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above causal graph shows the assumptions encoded in the causal model. We can now use this graph to first identify \n", "the causal effect (go from a causal estimand to a probability expression), and then estimate the causal effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DoWhy philosophy: Keep identification and estimation separate\n", "\n", "Identification can be achieved without access to the data, acccesing only the graph. This results in an expression to be computed. This expression can then be evaluated using the available data in the estimation step.\n", "It is important to understand that these are orthogonal steps.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the parameter flag *proceed\\_when\\_unidentifiable*. It needs to be set to *True* to convey the assumption that we are ignoring any unobserved confounding. The default behavior is to prompt the user to double-check that the unobserved confounders can be ignored. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "causal_estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\")\n", "print(causal_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can input additional parameters to the estimate_effect method. For instance, to estimate the effect on any subset of the units, you can specify the \"target_units\" parameter which can be a string (\"ate\", \"att\", or \"atc\"), lambda function that filters rows of the data frame, or a new dataframe on which to compute the effect. You can also specify \"effect modifiers\" to estimate heterogeneous effects across these variables. See `help(CausalModel.estimate_effect)`. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Causal effect on the control group (ATC)\n", "causal_estimate_att = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\",\n", " target_units = \"atc\")\n", "print(causal_estimate_att)\n", "print(\"Causal Estimate is \" + str(causal_estimate_att.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interface 2: Specify common causes and instruments" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Without graph \n", "model= CausalModel( \n", " data=df, \n", " treatment=data[\"treatment_name\"], \n", " outcome=data[\"outcome_name\"], \n", " common_causes=data[\"common_causes_names\"],\n", " effect_modifiers=data[\"effect_modifier_names\"]) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get the same causal graph. Now identification and estimation is done as before.\n", "\n", "#### Identification" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate = model.estimate_effect(identified_estimand,\n", " method_name=\"backdoor.propensity_score_stratification\") \n", "print(estimate)\n", "print(\"Causal Estimate is \" + str(estimate.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate\n", "\n", "Let us now look at ways of refuting the estimate obtained. Refutation methods provide tests that every correct estimator should pass. So if an estimator fails the refutation test (p-value is <0.05), then it means that there is some problem with the estimator. \n", "\n", "Note that we cannot verify that the estimate is correct, but we can reject it if it violates certain expected behavior (this is analogous to scientific theories that can be falsified but not proven true). The below refutation tests are based on either \n", " 1) **Invariant transformations**: changes in the data that should not change the estimate. Any estimator whose result varies significantly between the original data and the modified data fails the test; \n", " \n", " a) Random Common Cause\n", " \n", " b) Data Subset\n", " \n", " \n", " 2) **Nullifying transformations**: after the data change, the causal true estimate is zero. Any estimator whose result varies significantly from zero on the new data fails the test.\n", " \n", " a) Placebo Treatment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\", show_progress_bar=True)\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"placebo_treatment_refuter\", show_progress_bar=True, placebo_type=\"permute\")\n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the propensity score stratification estimator is reasonably robust to refutations.\n", "\n", "**Reproducability**: For reproducibility, you can add a parameter \"random_seed\" to any refutation method, as shown below.\n", "\n", "**Parallelization**: You can also use built-in parallelization to speed up the refutation process. Simply set `n_jobs` to a value greater than 1 to spread the workload to multiple CPUs, or set `n_jobs=-1` to use all CPUs. Currently, this is available only for `random_common_cause`, `placebo_treatment_refuter`, and `data_subset_refuter`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, estimate,\n", " method_name=\"data_subset_refuter\", show_progress_bar=True, subset_fraction=0.9, random_seed = 1, n_jobs=-1, verbose=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable\n", "\n", "This refutation does not return a p-value. Instead, it provides a _sensitivity_ test on how quickly the estimate changes if the identifying assumptions (used in `identify_effect`) are not valid. Specifically, it checks sensitivity to violation of the backdoor assumption: that all common causes are observed. \n", "\n", "To do so, it creates a new dataset with an additional common cause between treatment and outcome. To capture the effect of the common cause, the method takes as input the strength of common cause's effect on treatment and outcome. Based on these inputs on the common cause's effects, it changes the treatment and outcome values and then reruns the estimator. The hope is that the new estimate does not change drastically with a small effect of the unobserved common cause, indicating a robustness to any unobserved confounding.\n", "\n", "Another equivalent way of interpreting this procedure is to assume that there was already unobserved confounding present in the input data. The change in treatment and outcome values _removes_ the effect of whatever unobserved common cause was present in the original data. Then rerunning the estimator on this modified data provides the correct identified estimate and we hope that the difference between the new estimate and the original estimate is not too high, for some bounded value of the unobserved common cause's effect.\n", "\n", "**Importance of domain knowledge**: This test requires _domain knowledge_ to set plausible input values of the effect of unobserved confounding. We first show the result for a single value of confounder's effect on treatment and outcome." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is often more useful to inspect the trend as the effect of unobserved confounding is increased. For that, we can provide an array of hypothesized confounders' effects. The output is the *(min, max)* range of the estimated effects under different unobserved confounding." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=np.array([0.001, 0.005, 0.01, 0.02]), effect_strength_on_outcome=0.01)\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above plot shows how the estimate decreases as the hypothesized confounding on treatment increases. By domain knowledge, we may know the maximum plausible confounding effect on treatment. Since we see that the effect does not go beyond zero, we can safely conclude that the causal effect of treatment `v0` is positive.\n", "\n", "We can also vary the confounding effect on both treatment and outcome. We obtain a heatmap." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_range=model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=[0.001, 0.005, 0.01, 0.02], \n", " effect_strength_on_outcome=[0.001, 0.005, 0.01,0.02])\n", "print(res_unobserved_range)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Automatically inferring effect strength parameters.** Finally, DoWhy supports automatic selection of the effect strength parameters. This is based on an assumption that the effect of the unobserved confounder on treatment or outcome cannot be stronger than that of any observed confounder. That is, we have collected data at least for the most relevant confounder. If that is the case, then we can bound the range of `effect_strength_on_treatment` and `effect_strength_on_outcome` by the effect strength of observed confounders. There is an additional optional parameter signifying whether the effect strength of unobserved confounder should be as high as the highest observed, or a fraction of it. You can set it using the optional `effect_fraction_on_treatment` and `effect_fraction_on_outcome` parameters. By default, these two parameters are 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved_auto = model.refute_estimate(identified_estimand, estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"binary_flip\", confounders_effect_on_outcome=\"linear\")\n", "print(res_unobserved_auto)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**: Assuming that the unobserved confounder does not affect the treatment or outcome more strongly than any observed confounder, the causal effect can be concluded to be positive." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Done

petergtz

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/example_notebooks/nb_index.rst

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

nice thought to add the level. for the second bullet (API), given that the APIs will likely merge in the future, how about calling it a "Task"? We can think of effect estimation and Intervention via GCM as the two tasks here. Edit: seeing the later examples, "Root Cause Analysis" may also fit nicely as a "Task" that we support.

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/example_notebooks/nb_index.rst

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

this one is "advanced"

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/example_notebooks/nb_index.rst

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

the conditional effects notebook (dowhy-conditional-treatment-effects) is a key one that introduces users to compute the conditional causal effect. Given that many people use doWhy to estimate the conditional effect, one option is to include it in the "introductory examples" section. We can mark it as Level: Beginner and Task: Conditional effect estimation. Thoughts?

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/example_notebooks/nb_index.rst

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

You're right. Originally, my thought was that there is the DoSampler API, GCM, and DoWhy's original "standard API", but we should make this forward-looking and we really want to focus on the tasks that users want to accomplish. 👍

petergtz

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/example_notebooks/nb_index.rst

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

Example notebooks ================= These examples are also available on `GitHub <https://github .com/py-why/dowhy/tree/main/docs/source/example_notebooks>`_. You can `run them locally <https://docs.jupyter .org/en/latest/running.html>`_ after cloning `DoWhy <https://github.com/py-why/dowhy>`_ and `installing Jupyter <https://jupyter.org/install>`_. Or you can run them directly in a web browser using the `Binder environment <https://mybinder.org/v2/gh/microsoft/dowhy/main?filepath=docs%2Fsource%2F>`_. Introductory examples --------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_simple_example` .. image:: ../_static/effect-estimation-estimand-expression.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy-conditional-treatment-effects` +++ | **Level:** Beginner | **Task:** Conditional effect estimation .. card:: :doc:`gcm_basic_example` .. image:: ../_static/graph-xyz.png :width: 50px :align: center +++ | **Level:** Beginner | **Task:** Intervention via GCM Real world-inspired examples ---------------------------- .. card-carousel:: 3 .. card:: :doc:`DoWhy-The Causal Story Behind Hotel Booking Cancellations` .. image:: ../_static/hotel-bookings.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`dowhy_example_effect_of_memberrewards_program` .. image:: ../_static/membership-program-graph.png +++ | **Level:** Beginner | **Task:** Effect estimation .. card:: :doc:`gcm_rca_microservice_architecture` .. image:: ../_static/microservice-architecture.png +++ | **Level:** Beginner | **Task:** Root cause analysis, intervention via GCM .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** Intervention via GCM .. card:: :doc:`gcm_supply_chain_dist_change` .. image:: ../_static/supply-chain.png +++ | **Level:** Advanced | **Task:** Root cause analysis via GCM .. card:: :doc:`gcm_counterfactual_medical_dry_eyes` +++ | **Level:** Advanced | **Task:** Counterfactuals via GCM Examples on benchmarks datasets ------------------------------- .. card-carousel:: 3 .. card:: :doc:`dowhy_ihdp_data_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_lalonde_example` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`dowhy_refutation_testing` +++ | **Level:** Advanced | **Task:** Effect inference .. card:: :doc:`gcm_401k_analysis` +++ | **Level:** Advanced | **Task:** GCM inference .. card:: :doc:`lalonde_pandas_api` +++ | **Level:** Advanced | **Task:** Do Sampler Miscellaneous ------------- .. card-carousel:: 3 .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`load_graph_example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`gcm_draw_samples` +++ | **Level:** Beginner | **Task:** GCM inference .. card:: :doc:`dowhy-simple-iv-example` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`graph_conditional_independence_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_demo_dummy_outcome_refuter` +++ | **Level:** Beginner | **Task:** Effect inference .. card:: :doc:`dowhy_multiple_treatments` +++ | **Level:** Advanced | **Task:** Effect inference .. toctree:: :maxdepth: 1 :caption: Introductory examples :hidden: dowhy_simple_example gcm_basic_example dowhy_confounder_example dowhy_estimation_methods dowhy_interpreter dowhy_causal_discovery_example dowhy-conditional-treatment-effects dowhy_mediation_analysis dowhy_refuter_notebook dowhy_causal_api do_sampler_demo .. toctree:: :maxdepth: 1 :caption: Real world-inspired examples :hidden: DoWhy-The Causal Story Behind Hotel Booking Cancellations dowhy_example_effect_of_memberrewards_program gcm_rca_microservice_architecture gcm_401k_analysis gcm_supply_chain_dist_change gcm_counterfactual_medical_dry_eyes .. toctree:: :maxdepth: 1 :caption: Examples on benchmarks datasets :hidden: dowhy_ihdp_data_example dowhy_lalonde_example dowhy_refutation_testing gcm_401k_analysis lalonde_pandas_api .. toctree:: :maxdepth: 1 :caption: Miscellaneous :hidden: load_graph_example gcm_draw_samples dowhy-simple-iv-example graph_conditional_independence_refuter dowhy_demo_dummy_outcome_refuter dowhy_multiple_treatments identifying_effects_using_id_algorithm.ipynb

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Added

petergtz

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

cool title 👍

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

typo: model.

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

we also use causal graphs for effect identification step. Since the two frameworks are mentioned above, I guess we can focus on an end-user's perspective here. Maybe rephrase it to, "For effect inference, DoWhy offers a 4-step recipe consisting of modeling a causal graph, identification, estimation, and refutation. The four steps are designed to explicitly bring out the assumptions in a causal analysis and then validate them in the refutation step. DoWhy supports estimation of both average and conditional causal effects.

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

haha, this might be too aggressive? How about, To understand what these four steps mean (and why we need four steps), the best place to learn more is the user's guide ... chapter. Alternatively, you can dive into the code and explore basic features in the doc notebook."

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

given the new structure, should the further resources go into the user guide section where we talk about causality?

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

at this point, it will also be good to highlight the fact that we interface with EconML for conditional effects, since people have found that integration useful. We can add a sentence like, "For estimation of conditional effects, you can also use methods from EconML using the same API, refer to this [notebook](dowhy-conditional-treatment-effects).

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

This actually not a new formulation, but an existing one: - https://www.pywhy.org/dowhy/v0.8/user_guide/causality_intro.html?highlight=estimation - https://www.pywhy.org/dowhy/main/getting_started/index.html#next-steps I do get your point though. Alternative suggestion: Kailash and I have already started working restructuring our User guide by shifting away the focus from the different APIs we currently have to specific tasks. This is not easy, but I think once we have that, we can also apply the same technique here in the Getting started section. Can we post-pone the improvement until then?

petergtz

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Yes, maybe. Have also already thought about the best place for this section. If it's okay, I would also like to post-pone this change until we have reworked the User Guide. Hopefully, that will give us a better understanding where this will fit.

petergtz

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Don e

petergtz

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Sounds good. We can postpone this.

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/getting_started/index.rst

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

Getting Started =============== Installation ^^^^^^^^^^^^ The simplest installation is through `pip <https://pypi.org/project/dowhy/>`__ or conda: .. tab-set-code:: .. code-block:: pip pip install dowhy .. code-block:: conda conda install -c conda-forge dowhy Further installation scenarios and instructions can be found at :doc:`install`. "Hello causal inference world" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this section, we will show the "Hello world" version of DoWhy. DoWhy is based on a simple unifying language for causal inference, unifying two powerful frameworks, namely graphical causal models (GCM) and potential outcomes (PO). It uses graph-based criteria and do-calculus for modeling assumptions and identifying a non-parametric causal effect. To get you started, we introduce two features out of a large variety of features DoWhy offers. Effect inference ---------------- For effect estimation, DoWhy switches to methods based primarily on potential outcomes. To do it, DoWhy offers a simple 4-step recipe consisting of modeling a causal model, identification, estimation, and refutation: .. code:: python from dowhy import CausalModel import dowhy.datasets # Generate some sample data data = dowhy.datasets.linear_dataset( beta=10, num_common_causes=5, num_instruments=2, num_samples=10000) # Step 1: Create a causal model from the data and given graph. model = CausalModel( data=data["df"], treatment=data["treatment_name"], outcome=data["outcome_name"], graph=data["gml_graph"]) # Step 2: Identify causal effect and return target estimands identified_estimand = model.identify_effect() # Step 3: Estimate the target estimand using a statistical method. estimate = model.estimate_effect(identified_estimand, method_name="backdoor.propensity_score_matching") # Step 4: Refute the obtained estimate using multiple robustness checks. refute_results = model.refute_estimate(identified_estimand, estimate, method_name="random_common_cause") To understand what these four steps mean (and why we need four steps), the best place to learn more is the user guide's :doc:`../user_guide/effect_inference/index` chapter. Alternatively, you can dive into the code and explore basic features in :doc:`../example_notebooks/dowhy_simple_example`. For estimation of conditional effects, you can also use methods from `EconML <https://github.com/microsoft/EconML>`_ using the same API, refer to :doc:`../example_notebooks/dowhy-conditional-treatment-effects`. Graphical causal model-based inference --------------------------------------- For features like root cause analysis, structural analysis and similar, DoWhy uses graphical causal models. The language of graphical causal models again offers a variety of causal questions that can be answered. DoWhy's API to answer these causal questions follows a simple 3-step recipe as follows: .. code:: python import networkx as nx, numpy as np, pandas as pd from dowhy import gcm # Let's generate some "normal" data we assume we're given from our problem domain: X = np.random.normal(loc=0, scale=1, size=1000) Y = 2 * X + np.random.normal(loc=0, scale=1, size=1000) Z = 3 * Y + np.random.normal(loc=0, scale=1, size=1000) data = pd.DataFrame(dict(X=X, Y=Y, Z=Z)) # Step 1: Model our system: causal_model = gcm.StructuralCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) gcm.auto.assign_causal_mechanisms(causal_model, data) # Step 2: Train our causal model with the data from above: gcm.fit(causal_model, data) # Step 3: Perform a causal analysis. E.g. we have an: anomalous_record = pd.DataFrame(dict(X=[.7], Y=[100.0], Z=[303.0])) # ... and would like to answer the question: # "Which node is the root cause of the anomaly in Z?": anomaly_attribution = gcm.attribute_anomalies(causal_model, "Z", anomalous_record) Again, if this doesn't entirely make sense, yet, we recommend starting with :doc:`../user_guide/gcm_based_inference/index` in the user guide or check out :doc:`../example_notebooks/gcm_basic_example`. Further resources ^^^^^^^^^^^^^^^^^ There's further resources available: - A `Tutorial on causal inference <https://github.com/amit-sharma/causal-inference-tutorial/>`_ - A comprehensive `Tutorial on Causal Inference and Counterfactual Reasoning <https://causalinference.gitlab.io/kdd-tutorial/>`_ at the `ACM Knowledge Discovery and Data Mining 2018 conference <http://www.kdd.org/kdd2018/>`_ - A video introduction to the four steps of causal inference and its implications for machine learning from Microsoft Research: `Foundations of causal inference and its impacts on machine learning <https://note.microsoft.com/MSR-Webinar-DoWhy-Library-Registration-On-Demand.html>`_ - The PDF book `Elements of Causal Inference <https://mitp-content-server.mit.edu/books/content/sectbyfn?collid=books_pres_0&id=11283&fn=11283.pdf>`_

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Sounds good!

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/index.rst

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo **Date**: |today| **Version**: |version| **Related resources**: `Source Repository <https://github.com/py-why/dowhy>`__ | `Issues & Ideas <https://github.com/py-why/dowhy/issues>`__ | `Join the Community (Discord) <https://discord.gg/cSBGb3vsZb>`__ `PyWhy Organization <https://www.pywhy.org>`__ | `DoWhy on PyPI <https://pypi.org/project/dowhy>`__ | Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. .. grid:: 1 2 2 2 :gutter: 4 .. grid-item-card:: Getting started :shadow: md :link: getting_started/index :link-type: doc :octicon:`rocket;2em;sd-text-info` ^^^ New to DoWhy? Our Getting started guide will get you up to speed in minutes. It'll help you install DoWhy and write your first lines of code. Once completed, you'll be ready to the run examples and follow along in the User Guide. .. grid-item-card:: User Guide :shadow: md :link: user_guide/intro :link-type: doc :octicon:`book;2em;sd-text-info` ^^^ Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive User Guide. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. .. grid-item-card:: Examples :shadow: md :link: example_notebooks/nb_index :link-type: doc :octicon:`video;2em;sd-text-info` ^^^ If you prefer to learn by example, we recommend to browse the examples. It covers a wide variety of problems that you can use to liken to your own problem. .. grid-item-card:: API Reference :shadow: md :link: dowhy :link-type: doc :octicon:`code;2em;sd-text-info` ^^^ The API reference contains a detailed description of the functions, modules, and objects included in DoWhy. It assumes that you have an understanding of the key concepts.

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo **Date**: |today| **Version**: |version| **Related resources**: `Source Repository <https://github.com/py-why/dowhy>`__ | `Issues & Ideas <https://github.com/py-why/dowhy/issues>`__ | `Join the Community (Discord) <https://discord.gg/cSBGb3vsZb>`__ `PyWhy Organization <https://www.pywhy.org>`__ | `DoWhy on PyPI <https://pypi.org/project/dowhy>`__ | Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. .. grid:: 1 2 2 2 :gutter: 4 .. grid-item-card:: Getting started :shadow: md :link: getting_started/index :link-type: doc :octicon:`rocket;2em;sd-text-info` ^^^ New to DoWhy? Our Getting started guide will get you up to speed in minutes. It'll help you install DoWhy and write your first lines of code. Once completed, you'll be ready to the run examples and follow along in the User Guide. .. grid-item-card:: User Guide :shadow: md :link: user_guide/intro :link-type: doc :octicon:`book;2em;sd-text-info` ^^^ Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive User Guide. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. .. grid-item-card:: Examples :shadow: md :link: example_notebooks/nb_index :link-type: doc :octicon:`video;2em;sd-text-info` ^^^ If you prefer to learn by example, we recommend to browse the examples. It covers a wide variety of problems that you can use to liken to your own problem. .. grid-item-card:: API Reference :shadow: md :link: dowhy :link-type: doc :octicon:`code;2em;sd-text-info` ^^^ The API reference contains a detailed description of the functions, modules, and objects included in DoWhy. It assumes that you have an understanding of the key concepts.

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

love this new sentence +1

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/index.rst

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo **Date**: |today| **Version**: |version| **Related resources**: `Source Repository <https://github.com/py-why/dowhy>`__ | `Issues & Ideas <https://github.com/py-why/dowhy/issues>`__ | `Join the Community (Discord) <https://discord.gg/cSBGb3vsZb>`__ `PyWhy Organization <https://www.pywhy.org>`__ | `DoWhy on PyPI <https://pypi.org/project/dowhy>`__ | Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. .. grid:: 1 2 2 2 :gutter: 4 .. grid-item-card:: Getting started :shadow: md :link: getting_started/index :link-type: doc :octicon:`rocket;2em;sd-text-info` ^^^ New to DoWhy? Our Getting started guide will get you up to speed in minutes. It'll help you install DoWhy and write your first lines of code. Once completed, you'll be ready to the run examples and follow along in the User Guide. .. grid-item-card:: User Guide :shadow: md :link: user_guide/intro :link-type: doc :octicon:`book;2em;sd-text-info` ^^^ Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive User Guide. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. .. grid-item-card:: Examples :shadow: md :link: example_notebooks/nb_index :link-type: doc :octicon:`video;2em;sd-text-info` ^^^ If you prefer to learn by example, we recommend to browse the examples. It covers a wide variety of problems that you can use to liken to your own problem. .. grid-item-card:: API Reference :shadow: md :link: dowhy :link-type: doc :octicon:`code;2em;sd-text-info` ^^^ The API reference contains a detailed description of the functions, modules, and objects included in DoWhy. It assumes that you have an understanding of the key concepts.

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo **Date**: |today| **Version**: |version| **Related resources**: `Source Repository <https://github.com/py-why/dowhy>`__ | `Issues & Ideas <https://github.com/py-why/dowhy/issues>`__ | `Join the Community (Discord) <https://discord.gg/cSBGb3vsZb>`__ `PyWhy Organization <https://www.pywhy.org>`__ | `DoWhy on PyPI <https://pypi.org/project/dowhy>`__ | Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. .. grid:: 1 2 2 2 :gutter: 4 .. grid-item-card:: Getting started :shadow: md :link: getting_started/index :link-type: doc :octicon:`rocket;2em;sd-text-info` ^^^ New to DoWhy? Our Getting started guide will get you up to speed in minutes. It'll help you install DoWhy and write your first lines of code. Once completed, you'll be ready to the run examples and follow along in the User Guide. .. grid-item-card:: User Guide :shadow: md :link: user_guide/intro :link-type: doc :octicon:`book;2em;sd-text-info` ^^^ Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive User Guide. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. .. grid-item-card:: Examples :shadow: md :link: example_notebooks/nb_index :link-type: doc :octicon:`video;2em;sd-text-info` ^^^ If you prefer to learn by example, we recommend to browse the examples. It covers a wide variety of problems that you can use to liken to your own problem. .. grid-item-card:: API Reference :shadow: md :link: dowhy :link-type: doc :octicon:`code;2em;sd-text-info` ^^^ The API reference contains a detailed description of the functions, modules, and objects included in DoWhy. It assumes that you have an understanding of the key concepts.

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Some of these are action links (check the source, raise an issue), so it may be worth putting them first. Source Repo | Issues and Ideas | Join the community (Discord) | PyWhy organization | DoWhy on PyPI

amit-sharma

py-why/dowhy

Restructure documentation

The result of this can be seen at https://petergtz.github.io/dowhy/main - Add logo to docs and README - Move 4-step process documentation from docs landing page to effect inference user guide - Provide documentation overview on docs starting page. - Move citation page from docs landing page to user guide - Introduce cards on docs landing page - Move effect inference comparison to effect inference user guide - Restructure Getting Started page - Simplify installation instructions, refer to detailed installation instructions on dedicated page - Introduce Hello World-like code samples - Introduce cards-carousel for example page **Note:** When merging this PR, please do not squash. I deliberately kept the commits clean and each stands on its own. The history will stay clearer when the commits are not squashed into one.

2022-11-11 14:23:31+00:00

2022-11-17 13:13:21+00:00

docs/source/index.rst

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo **Date**: |today| **Version**: |version| **Related resources**: `Source Repository <https://github.com/py-why/dowhy>`__ | `Issues & Ideas <https://github.com/py-why/dowhy/issues>`__ | `Join the Community (Discord) <https://discord.gg/cSBGb3vsZb>`__ `PyWhy Organization <https://www.pywhy.org>`__ | `DoWhy on PyPI <https://pypi.org/project/dowhy>`__ | Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. .. grid:: 1 2 2 2 :gutter: 4 .. grid-item-card:: Getting started :shadow: md :link: getting_started/index :link-type: doc :octicon:`rocket;2em;sd-text-info` ^^^ New to DoWhy? Our Getting started guide will get you up to speed in minutes. It'll help you install DoWhy and write your first lines of code. Once completed, you'll be ready to the run examples and follow along in the User Guide. .. grid-item-card:: User Guide :shadow: md :link: user_guide/intro :link-type: doc :octicon:`book;2em;sd-text-info` ^^^ Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive User Guide. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. .. grid-item-card:: Examples :shadow: md :link: example_notebooks/nb_index :link-type: doc :octicon:`video;2em;sd-text-info` ^^^ If you prefer to learn by example, we recommend to browse the examples. It covers a wide variety of problems that you can use to liken to your own problem. .. grid-item-card:: API Reference :shadow: md :link: dowhy :link-type: doc :octicon:`code;2em;sd-text-info` ^^^ The API reference contains a detailed description of the functions, modules, and objects included in DoWhy. It assumes that you have an understanding of the key concepts.

DoWhy documentation =================== .. toctree:: :maxdepth: 3 :hidden: :glob: getting_started/index User Guide <user_guide/index> Examples <example_notebooks/nb_index> dowhy Contributing <contributing> code_repo **Date**: |today| **Version**: |version| **Related resources**: `Source Repository <https://github.com/py-why/dowhy>`__ | `Issues & Ideas <https://github.com/py-why/dowhy/issues>`__ | `Join the Community (Discord) <https://discord.gg/cSBGb3vsZb>`__ `PyWhy Organization <https://www.pywhy.org>`__ | `DoWhy on PyPI <https://pypi.org/project/dowhy>`__ | Much like machine learning libraries have done for prediction, DoWhy is a Python library that aims to spark causal thinking and analysis. DoWhy provides a wide variety of algorithms for effect estimation, causal structure learning, diagnosis of causal structures, root cause analysis, interventions and counterfactuals. .. grid:: 1 2 2 2 :gutter: 4 .. grid-item-card:: Getting started :shadow: md :link: getting_started/index :link-type: doc :octicon:`rocket;2em;sd-text-info` ^^^ New to DoWhy? Our Getting started guide will get you up to speed in minutes. It'll help you install DoWhy and write your first lines of code. Once completed, you'll be ready to the run examples and follow along in the User Guide. .. grid-item-card:: User Guide :shadow: md :link: user_guide/intro :link-type: doc :octicon:`book;2em;sd-text-info` ^^^ Complete newbie when it comes to causal inference and DoWhy? Then you probably want to read our comprehensive User Guide. It guides you through everything you need to know, including the concepts and science you need to know when trying to solve non-trivial problems. .. grid-item-card:: Examples :shadow: md :link: example_notebooks/nb_index :link-type: doc :octicon:`video;2em;sd-text-info` ^^^ If you prefer to learn by example, we recommend to browse the examples. It covers a wide variety of problems that you can use to liken to your own problem. .. grid-item-card:: API Reference :shadow: md :link: dowhy :link-type: doc :octicon:`code;2em;sd-text-info` ^^^ The API reference contains a detailed description of the functions, modules, and objects included in DoWhy. It assumes that you have an understanding of the key concepts.

petergtz

30c102e358258b103fec8cd3ce42de9cf2051a50

de8969a5c100e5186f7892f16073129b6d0cffc6

Done

petergtz

py-why/dowhy

Functional api/causal estimators

* Introduce `fit()` method to estimators. * Refactor constructors to avoid using `*args` and `**kwargs` and have more explicit parameters. * Refactor refuters and other parts of the code to use `fit()` and modify arguments to `estimate_effect()`

2022-11-04 16:15:39+00:00

2022-12-03 17:07:53+00:00

docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Conditional Average Treatment Effects (CATE) with DoWhy and EconML\n", "\n", "This is an experimental feature where we use [EconML](https://github.com/microsoft/econml) methods from DoWhy. Using EconML allows CATE estimation using different methods. \n", "\n", "All four steps of causal inference in DoWhy remain the same: model, identify, estimate, and refute. The key difference is that we now call econml methods in the estimation step. There is also a simpler example using linear regression to understand the intuition behind CATE estimators. \n", "\n", "All datasets are generated using linear structural equations.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import logging\n", "\n", "import dowhy\n", "from dowhy import CausalModel\n", "import dowhy.datasets\n", "\n", "import econml\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "BETA = 10" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " num_treatments=1,\n", " treatment_is_binary=False,\n", " num_discrete_common_causes=2,\n", " num_discrete_effect_modifiers=0,\n", " one_hot_encode=False)\n", "df=data['df']\n", "print(df.head())\n", "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = CausalModel(data=data[\"df\"], \n", " treatment=data[\"treatment_name\"], outcome=data[\"outcome_name\"], \n", " graph=data[\"gml_graph\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "identified_estimand= model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Model \n", "First, let us build some intuition using a linear model for estimating CATE. The effect modifiers (that lead to a heterogeneous treatment effect) can be modeled as interaction terms with the treatment. Thus, their value modulates the effect of treatment. \n", "\n", "Below the estimated effect of changing treatment from 0 to 1. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "linear_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.linear_regression\",\n", " control_value=0,\n", " treatment_value=1)\n", "print(linear_estimate) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## EconML methods\n", "We now move to the more advanced methods from the EconML package for estimating CATE.\n", "\n", "First, let us look at the double machine learning estimator. Method_name corresponds to the fully qualified name of the class that we want to use. For double ML, it is \"econml.dml.DML\". \n", "\n", "Target units defines the units over which the causal estimate is to be computed. This can be a lambda function filter on the original dataframe, a new Pandas dataframe, or a string corresponding to the three main kinds of target units (\"ate\", \"att\" and \"atc\"). Below we show an example of a lambda function. \n", "\n", "Method_params are passed directly to EconML. For details on allowed parameters, refer to the EconML documentation. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = lambda df: df[\"X0\"]>1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=False)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = 1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### CATE Object and Confidence Intervals\n", "EconML provides its own methods to compute confidence intervals. Using BootstrapInference in the example below. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "from econml.inference import BootstrapInference\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = \"ate\",\n", " confidence_intervals=True,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\": LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{\n", " 'inference': BootstrapInference(n_bootstrap_samples=100, n_jobs=-1),\n", " }\n", " })\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can provide a new inputs as target units and estimate CATE on them." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "test_cols= data['effect_modifier_names'] # only need effect modifiers' values\n", "test_arr = [np.random.uniform(0,1, 10) for _ in range(len(test_cols))] # all variables are sampled uniformly, sample of 10\n", "test_df = pd.DataFrame(np.array(test_arr).transpose(), columns=test_cols)\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = test_df,\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}\n", " })\n", "print(dml_estimate.cate_estimates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can also retrieve the raw EconML estimator object for any further operations" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dml_estimate._estimator_object)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Works with any EconML method\n", "In addition to double machine learning, below we example analyses using orthogonal forests, DRLearner (bug to fix), and neural network-based instrumental variables. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Binary treatment, Binary outcome" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_binary = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " treatment_is_binary=True, outcome_is_binary=True)\n", "# convert boolean values to {0,1} numeric\n", "data_binary['df'].v0 = data_binary['df'].v0.astype(int)\n", "data_binary['df'].y = data_binary['df'].y.astype(int)\n", "print(data_binary['df'])\n", "\n", "model_binary = CausalModel(data=data_binary[\"df\"], \n", " treatment=data_binary[\"treatment_name\"], outcome=data_binary[\"outcome_name\"], \n", " graph=data_binary[\"gml_graph\"])\n", "identified_estimand_binary = model_binary.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using DRLearner estimator" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LogisticRegressionCV\n", "#todo needs binary y\n", "drlearner_estimate = model_binary.estimate_effect(identified_estimand_binary, \n", " method_name=\"backdoor.econml.drlearner.LinearDRLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'model_propensity': LogisticRegressionCV(cv=3, solver='lbfgs', multi_class='auto')\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(drlearner_estimate)\n", "print(\"True causal estimate is\", data_binary[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Instrumental Variable Method" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import keras\n", "from econml.deepiv import DeepIVEstimator\n", "dims_zx = len(model.get_instruments())+len(model.get_effect_modifiers())\n", "dims_tx = len(model._treatment)+len(model.get_effect_modifiers())\n", "treatment_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_zx,)), # sum of dims of Z and X \n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17)]) \n", "response_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_tx,)), # sum of dims of T and X\n", " keras.layers.Dropout(0.17), \n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(1)])\n", "\n", "deepiv_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"iv.econml.deepiv.DeepIV\",\n", " target_units = lambda df: df[\"X0\"]>-1, \n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'n_components': 10, # Number of gaussians in the mixture density networks\n", " 'm': lambda z, x: treatment_model(keras.layers.concatenate([z, x])), # Treatment model,\n", " \"h\": lambda t, x: response_model(keras.layers.concatenate([t, x])), # Response model\n", " 'n_samples': 1, # Number of samples used to estimate the response\n", " 'first_stage_options': {'epochs':25},\n", " 'second_stage_options': {'epochs':25}\n", " },\n", " \"fit_params\":{}})\n", "print(deepiv_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metalearners" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_experiment = dowhy.datasets.linear_dataset(BETA, num_common_causes=5, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=5,\n", " treatment_is_binary=True, outcome_is_binary=False)\n", "# convert boolean values to {0,1} numeric\n", "data_experiment['df'].v0 = data_experiment['df'].v0.astype(int)\n", "print(data_experiment['df'])\n", "model_experiment = CausalModel(data=data_experiment[\"df\"], \n", " treatment=data_experiment[\"treatment_name\"], outcome=data_experiment[\"outcome_name\"], \n", " graph=data_experiment[\"gml_graph\"])\n", "identified_estimand_experiment = model_experiment.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.ensemble import RandomForestRegressor\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'models': RandomForestRegressor()\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Avoiding retraining the estimator " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once an estimator is fitted, it can be reused to estimate effect on different data points. In this case, you can pass `fit_estimator=False` to `estimate_effect`. This works for any EconML estimator. We show an example for the T-learner below." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# For metalearners, need to provide all the features (except treatmeant and outcome)\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " fit_estimator=False,\n", " target_units=data_experiment[\"df\"].drop([\"v0\",\"y\", \"Z0\", \"Z1\"], axis=1)[9995:], \n", " method_params={})\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"random_common_cause\")\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"linear\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\",\n", " num_simulations=10 # at least 100 is good, setting to 10 for speed \n", " ) \n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.8,\n", " num_simulations=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More refutation methods to come, especially specific to the CATE estimators." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.12" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Conditional Average Treatment Effects (CATE) with DoWhy and EconML\n", "\n", "This is an experimental feature where we use [EconML](https://github.com/microsoft/econml) methods from DoWhy. Using EconML allows CATE estimation using different methods. \n", "\n", "All four steps of causal inference in DoWhy remain the same: model, identify, estimate, and refute. The key difference is that we now call econml methods in the estimation step. There is also a simpler example using linear regression to understand the intuition behind CATE estimators. \n", "\n", "All datasets are generated using linear structural equations.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import logging\n", "\n", "import dowhy\n", "from dowhy import CausalModel\n", "import dowhy.datasets\n", "\n", "import econml\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "BETA = 10" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " num_treatments=1,\n", " treatment_is_binary=False,\n", " num_discrete_common_causes=2,\n", " num_discrete_effect_modifiers=0,\n", " one_hot_encode=False)\n", "df=data['df']\n", "print(df.head())\n", "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = CausalModel(data=data[\"df\"], \n", " treatment=data[\"treatment_name\"], outcome=data[\"outcome_name\"], \n", " graph=data[\"gml_graph\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "identified_estimand= model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Model \n", "First, let us build some intuition using a linear model for estimating CATE. The effect modifiers (that lead to a heterogeneous treatment effect) can be modeled as interaction terms with the treatment. Thus, their value modulates the effect of treatment. \n", "\n", "Below the estimated effect of changing treatment from 0 to 1. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "linear_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.linear_regression\",\n", " control_value=0,\n", " treatment_value=1)\n", "print(linear_estimate) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## EconML methods\n", "We now move to the more advanced methods from the EconML package for estimating CATE.\n", "\n", "First, let us look at the double machine learning estimator. Method_name corresponds to the fully qualified name of the class that we want to use. For double ML, it is \"econml.dml.DML\". \n", "\n", "Target units defines the units over which the causal estimate is to be computed. This can be a lambda function filter on the original dataframe, a new Pandas dataframe, or a string corresponding to the three main kinds of target units (\"ate\", \"att\" and \"atc\"). Below we show an example of a lambda function. \n", "\n", "Method_params are passed directly to EconML. For details on allowed parameters, refer to the EconML documentation. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = lambda df: df[\"X0\"]>1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=False)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = 1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### CATE Object and Confidence Intervals\n", "EconML provides its own methods to compute confidence intervals. Using BootstrapInference in the example below. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "from econml.inference import BootstrapInference\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = \"ate\",\n", " confidence_intervals=True,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\": LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{\n", " 'inference': BootstrapInference(n_bootstrap_samples=100, n_jobs=-1),\n", " }\n", " })\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can provide a new inputs as target units and estimate CATE on them." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "test_cols= data['effect_modifier_names'] # only need effect modifiers' values\n", "test_arr = [np.random.uniform(0,1, 10) for _ in range(len(test_cols))] # all variables are sampled uniformly, sample of 10\n", "test_df = pd.DataFrame(np.array(test_arr).transpose(), columns=test_cols)\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = test_df,\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}\n", " })\n", "print(dml_estimate.cate_estimates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can also retrieve the raw EconML estimator object for any further operations" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dml_estimate._estimator_object)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Works with any EconML method\n", "In addition to double machine learning, below we example analyses using orthogonal forests, DRLearner (bug to fix), and neural network-based instrumental variables. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Binary treatment, Binary outcome" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_binary = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " treatment_is_binary=True, outcome_is_binary=True)\n", "# convert boolean values to {0,1} numeric\n", "data_binary['df'].v0 = data_binary['df'].v0.astype(int)\n", "data_binary['df'].y = data_binary['df'].y.astype(int)\n", "print(data_binary['df'])\n", "\n", "model_binary = CausalModel(data=data_binary[\"df\"], \n", " treatment=data_binary[\"treatment_name\"], outcome=data_binary[\"outcome_name\"], \n", " graph=data_binary[\"gml_graph\"])\n", "identified_estimand_binary = model_binary.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using DRLearner estimator" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LogisticRegressionCV\n", "#todo needs binary y\n", "drlearner_estimate = model_binary.estimate_effect(identified_estimand_binary, \n", " method_name=\"backdoor.econml.dr.LinearDRLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'model_propensity': LogisticRegressionCV(cv=3, solver='lbfgs', multi_class='auto')\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(drlearner_estimate)\n", "print(\"True causal estimate is\", data_binary[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Instrumental Variable Method" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import keras\n", "dims_zx = len(model.get_instruments())+len(model.get_effect_modifiers())\n", "dims_tx = len(model._treatment)+len(model.get_effect_modifiers())\n", "treatment_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_zx,)), # sum of dims of Z and X \n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17)]) \n", "response_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_tx,)), # sum of dims of T and X\n", " keras.layers.Dropout(0.17), \n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(1)])\n", "\n", "deepiv_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"iv.econml.iv.nnet.DeepIV\",\n", " target_units = lambda df: df[\"X0\"]>-1, \n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'n_components': 10, # Number of gaussians in the mixture density networks\n", " 'm': lambda z, x: treatment_model(keras.layers.concatenate([z, x])), # Treatment model,\n", " \"h\": lambda t, x: response_model(keras.layers.concatenate([t, x])), # Response model\n", " 'n_samples': 1, # Number of samples used to estimate the response\n", " 'first_stage_options': {'epochs':25},\n", " 'second_stage_options': {'epochs':25}\n", " },\n", " \"fit_params\":{}})\n", "print(deepiv_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metalearners" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_experiment = dowhy.datasets.linear_dataset(BETA, num_common_causes=5, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=5,\n", " treatment_is_binary=True, outcome_is_binary=False)\n", "# convert boolean values to {0,1} numeric\n", "data_experiment['df'].v0 = data_experiment['df'].v0.astype(int)\n", "print(data_experiment['df'])\n", "model_experiment = CausalModel(data=data_experiment[\"df\"], \n", " treatment=data_experiment[\"treatment_name\"], outcome=data_experiment[\"outcome_name\"], \n", " graph=data_experiment[\"gml_graph\"])\n", "identified_estimand_experiment = model_experiment.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.ensemble import RandomForestRegressor\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'models': RandomForestRegressor()\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Avoiding retraining the estimator " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once an estimator is fitted, it can be reused to estimate effect on different data points. In this case, you can pass `fit_estimator=False` to `estimate_effect`. This works for any EconML estimator. We show an example for the T-learner below." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# For metalearners, need to provide all the features (except treatmeant and outcome)\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " fit_estimator=False,\n", " target_units=data_experiment[\"df\"].drop([\"v0\",\"y\", \"Z0\", \"Z1\"], axis=1)[9995:], \n", " method_params={})\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"random_common_cause\")\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"linear\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\",\n", " num_simulations=10 # at least 100 is good, setting to 10 for speed \n", " ) \n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.8,\n", " num_simulations=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More refutation methods to come, especially specific to the CATE estimators." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

andresmor-ms

11c4e0dafd6e824eb81ad14262457d954ae61468

affe0952f4aba6845247355c171565510c2c1673

obtaining a build error. can you change the import of deepiv too? "from econml.iv.nnet import DeepIV" CellExecutionError in example_notebooks/dowhy-conditional-treatment-effects.ipynb: [147](https://github.com/py-why/dowhy/actions/runs/3568922214/jobs/5998324083#step:6:148)------------------ [148](https://github.com/py-why/dowhy/actions/runs/3568922214/jobs/5998324083#step:6:149)import keras [149](https://github.com/py-why/dowhy/actions/runs/3568922214/jobs/5998324083#step:6:150)from econml.deepiv import DeepIVEstimator

amit-sharma

py-why/dowhy

Functional api/causal estimators

* Introduce `fit()` method to estimators. * Refactor constructors to avoid using `*args` and `**kwargs` and have more explicit parameters. * Refactor refuters and other parts of the code to use `fit()` and modify arguments to `estimate_effect()`

2022-11-04 16:15:39+00:00

2022-12-03 17:07:53+00:00

docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Conditional Average Treatment Effects (CATE) with DoWhy and EconML\n", "\n", "This is an experimental feature where we use [EconML](https://github.com/microsoft/econml) methods from DoWhy. Using EconML allows CATE estimation using different methods. \n", "\n", "All four steps of causal inference in DoWhy remain the same: model, identify, estimate, and refute. The key difference is that we now call econml methods in the estimation step. There is also a simpler example using linear regression to understand the intuition behind CATE estimators. \n", "\n", "All datasets are generated using linear structural equations.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import logging\n", "\n", "import dowhy\n", "from dowhy import CausalModel\n", "import dowhy.datasets\n", "\n", "import econml\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "BETA = 10" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " num_treatments=1,\n", " treatment_is_binary=False,\n", " num_discrete_common_causes=2,\n", " num_discrete_effect_modifiers=0,\n", " one_hot_encode=False)\n", "df=data['df']\n", "print(df.head())\n", "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = CausalModel(data=data[\"df\"], \n", " treatment=data[\"treatment_name\"], outcome=data[\"outcome_name\"], \n", " graph=data[\"gml_graph\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "identified_estimand= model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Model \n", "First, let us build some intuition using a linear model for estimating CATE. The effect modifiers (that lead to a heterogeneous treatment effect) can be modeled as interaction terms with the treatment. Thus, their value modulates the effect of treatment. \n", "\n", "Below the estimated effect of changing treatment from 0 to 1. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "linear_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.linear_regression\",\n", " control_value=0,\n", " treatment_value=1)\n", "print(linear_estimate) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## EconML methods\n", "We now move to the more advanced methods from the EconML package for estimating CATE.\n", "\n", "First, let us look at the double machine learning estimator. Method_name corresponds to the fully qualified name of the class that we want to use. For double ML, it is \"econml.dml.DML\". \n", "\n", "Target units defines the units over which the causal estimate is to be computed. This can be a lambda function filter on the original dataframe, a new Pandas dataframe, or a string corresponding to the three main kinds of target units (\"ate\", \"att\" and \"atc\"). Below we show an example of a lambda function. \n", "\n", "Method_params are passed directly to EconML. For details on allowed parameters, refer to the EconML documentation. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = lambda df: df[\"X0\"]>1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=False)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = 1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### CATE Object and Confidence Intervals\n", "EconML provides its own methods to compute confidence intervals. Using BootstrapInference in the example below. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "from econml.inference import BootstrapInference\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = \"ate\",\n", " confidence_intervals=True,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\": LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{\n", " 'inference': BootstrapInference(n_bootstrap_samples=100, n_jobs=-1),\n", " }\n", " })\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can provide a new inputs as target units and estimate CATE on them." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "test_cols= data['effect_modifier_names'] # only need effect modifiers' values\n", "test_arr = [np.random.uniform(0,1, 10) for _ in range(len(test_cols))] # all variables are sampled uniformly, sample of 10\n", "test_df = pd.DataFrame(np.array(test_arr).transpose(), columns=test_cols)\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = test_df,\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}\n", " })\n", "print(dml_estimate.cate_estimates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can also retrieve the raw EconML estimator object for any further operations" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dml_estimate._estimator_object)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Works with any EconML method\n", "In addition to double machine learning, below we example analyses using orthogonal forests, DRLearner (bug to fix), and neural network-based instrumental variables. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Binary treatment, Binary outcome" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_binary = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " treatment_is_binary=True, outcome_is_binary=True)\n", "# convert boolean values to {0,1} numeric\n", "data_binary['df'].v0 = data_binary['df'].v0.astype(int)\n", "data_binary['df'].y = data_binary['df'].y.astype(int)\n", "print(data_binary['df'])\n", "\n", "model_binary = CausalModel(data=data_binary[\"df\"], \n", " treatment=data_binary[\"treatment_name\"], outcome=data_binary[\"outcome_name\"], \n", " graph=data_binary[\"gml_graph\"])\n", "identified_estimand_binary = model_binary.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using DRLearner estimator" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LogisticRegressionCV\n", "#todo needs binary y\n", "drlearner_estimate = model_binary.estimate_effect(identified_estimand_binary, \n", " method_name=\"backdoor.econml.drlearner.LinearDRLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'model_propensity': LogisticRegressionCV(cv=3, solver='lbfgs', multi_class='auto')\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(drlearner_estimate)\n", "print(\"True causal estimate is\", data_binary[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Instrumental Variable Method" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import keras\n", "from econml.deepiv import DeepIVEstimator\n", "dims_zx = len(model.get_instruments())+len(model.get_effect_modifiers())\n", "dims_tx = len(model._treatment)+len(model.get_effect_modifiers())\n", "treatment_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_zx,)), # sum of dims of Z and X \n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17)]) \n", "response_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_tx,)), # sum of dims of T and X\n", " keras.layers.Dropout(0.17), \n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(1)])\n", "\n", "deepiv_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"iv.econml.deepiv.DeepIV\",\n", " target_units = lambda df: df[\"X0\"]>-1, \n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'n_components': 10, # Number of gaussians in the mixture density networks\n", " 'm': lambda z, x: treatment_model(keras.layers.concatenate([z, x])), # Treatment model,\n", " \"h\": lambda t, x: response_model(keras.layers.concatenate([t, x])), # Response model\n", " 'n_samples': 1, # Number of samples used to estimate the response\n", " 'first_stage_options': {'epochs':25},\n", " 'second_stage_options': {'epochs':25}\n", " },\n", " \"fit_params\":{}})\n", "print(deepiv_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metalearners" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_experiment = dowhy.datasets.linear_dataset(BETA, num_common_causes=5, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=5,\n", " treatment_is_binary=True, outcome_is_binary=False)\n", "# convert boolean values to {0,1} numeric\n", "data_experiment['df'].v0 = data_experiment['df'].v0.astype(int)\n", "print(data_experiment['df'])\n", "model_experiment = CausalModel(data=data_experiment[\"df\"], \n", " treatment=data_experiment[\"treatment_name\"], outcome=data_experiment[\"outcome_name\"], \n", " graph=data_experiment[\"gml_graph\"])\n", "identified_estimand_experiment = model_experiment.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.ensemble import RandomForestRegressor\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'models': RandomForestRegressor()\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Avoiding retraining the estimator " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once an estimator is fitted, it can be reused to estimate effect on different data points. In this case, you can pass `fit_estimator=False` to `estimate_effect`. This works for any EconML estimator. We show an example for the T-learner below." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# For metalearners, need to provide all the features (except treatmeant and outcome)\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " fit_estimator=False,\n", " target_units=data_experiment[\"df\"].drop([\"v0\",\"y\", \"Z0\", \"Z1\"], axis=1)[9995:], \n", " method_params={})\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"random_common_cause\")\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"linear\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\",\n", " num_simulations=10 # at least 100 is good, setting to 10 for speed \n", " ) \n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.8,\n", " num_simulations=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More refutation methods to come, especially specific to the CATE estimators." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.12" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Conditional Average Treatment Effects (CATE) with DoWhy and EconML\n", "\n", "This is an experimental feature where we use [EconML](https://github.com/microsoft/econml) methods from DoWhy. Using EconML allows CATE estimation using different methods. \n", "\n", "All four steps of causal inference in DoWhy remain the same: model, identify, estimate, and refute. The key difference is that we now call econml methods in the estimation step. There is also a simpler example using linear regression to understand the intuition behind CATE estimators. \n", "\n", "All datasets are generated using linear structural equations.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import logging\n", "\n", "import dowhy\n", "from dowhy import CausalModel\n", "import dowhy.datasets\n", "\n", "import econml\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "BETA = 10" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " num_treatments=1,\n", " treatment_is_binary=False,\n", " num_discrete_common_causes=2,\n", " num_discrete_effect_modifiers=0,\n", " one_hot_encode=False)\n", "df=data['df']\n", "print(df.head())\n", "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = CausalModel(data=data[\"df\"], \n", " treatment=data[\"treatment_name\"], outcome=data[\"outcome_name\"], \n", " graph=data[\"gml_graph\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "identified_estimand= model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Model \n", "First, let us build some intuition using a linear model for estimating CATE. The effect modifiers (that lead to a heterogeneous treatment effect) can be modeled as interaction terms with the treatment. Thus, their value modulates the effect of treatment. \n", "\n", "Below the estimated effect of changing treatment from 0 to 1. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "linear_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.linear_regression\",\n", " control_value=0,\n", " treatment_value=1)\n", "print(linear_estimate) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## EconML methods\n", "We now move to the more advanced methods from the EconML package for estimating CATE.\n", "\n", "First, let us look at the double machine learning estimator. Method_name corresponds to the fully qualified name of the class that we want to use. For double ML, it is \"econml.dml.DML\". \n", "\n", "Target units defines the units over which the causal estimate is to be computed. This can be a lambda function filter on the original dataframe, a new Pandas dataframe, or a string corresponding to the three main kinds of target units (\"ate\", \"att\" and \"atc\"). Below we show an example of a lambda function. \n", "\n", "Method_params are passed directly to EconML. For details on allowed parameters, refer to the EconML documentation. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = lambda df: df[\"X0\"]>1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=False)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = 1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### CATE Object and Confidence Intervals\n", "EconML provides its own methods to compute confidence intervals. Using BootstrapInference in the example below. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "from econml.inference import BootstrapInference\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = \"ate\",\n", " confidence_intervals=True,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\": LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{\n", " 'inference': BootstrapInference(n_bootstrap_samples=100, n_jobs=-1),\n", " }\n", " })\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can provide a new inputs as target units and estimate CATE on them." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "test_cols= data['effect_modifier_names'] # only need effect modifiers' values\n", "test_arr = [np.random.uniform(0,1, 10) for _ in range(len(test_cols))] # all variables are sampled uniformly, sample of 10\n", "test_df = pd.DataFrame(np.array(test_arr).transpose(), columns=test_cols)\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = test_df,\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}\n", " })\n", "print(dml_estimate.cate_estimates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can also retrieve the raw EconML estimator object for any further operations" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dml_estimate._estimator_object)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Works with any EconML method\n", "In addition to double machine learning, below we example analyses using orthogonal forests, DRLearner (bug to fix), and neural network-based instrumental variables. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Binary treatment, Binary outcome" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_binary = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " treatment_is_binary=True, outcome_is_binary=True)\n", "# convert boolean values to {0,1} numeric\n", "data_binary['df'].v0 = data_binary['df'].v0.astype(int)\n", "data_binary['df'].y = data_binary['df'].y.astype(int)\n", "print(data_binary['df'])\n", "\n", "model_binary = CausalModel(data=data_binary[\"df\"], \n", " treatment=data_binary[\"treatment_name\"], outcome=data_binary[\"outcome_name\"], \n", " graph=data_binary[\"gml_graph\"])\n", "identified_estimand_binary = model_binary.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using DRLearner estimator" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LogisticRegressionCV\n", "#todo needs binary y\n", "drlearner_estimate = model_binary.estimate_effect(identified_estimand_binary, \n", " method_name=\"backdoor.econml.dr.LinearDRLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'model_propensity': LogisticRegressionCV(cv=3, solver='lbfgs', multi_class='auto')\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(drlearner_estimate)\n", "print(\"True causal estimate is\", data_binary[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Instrumental Variable Method" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import keras\n", "dims_zx = len(model.get_instruments())+len(model.get_effect_modifiers())\n", "dims_tx = len(model._treatment)+len(model.get_effect_modifiers())\n", "treatment_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_zx,)), # sum of dims of Z and X \n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17)]) \n", "response_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_tx,)), # sum of dims of T and X\n", " keras.layers.Dropout(0.17), \n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(1)])\n", "\n", "deepiv_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"iv.econml.iv.nnet.DeepIV\",\n", " target_units = lambda df: df[\"X0\"]>-1, \n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'n_components': 10, # Number of gaussians in the mixture density networks\n", " 'm': lambda z, x: treatment_model(keras.layers.concatenate([z, x])), # Treatment model,\n", " \"h\": lambda t, x: response_model(keras.layers.concatenate([t, x])), # Response model\n", " 'n_samples': 1, # Number of samples used to estimate the response\n", " 'first_stage_options': {'epochs':25},\n", " 'second_stage_options': {'epochs':25}\n", " },\n", " \"fit_params\":{}})\n", "print(deepiv_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metalearners" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_experiment = dowhy.datasets.linear_dataset(BETA, num_common_causes=5, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=5,\n", " treatment_is_binary=True, outcome_is_binary=False)\n", "# convert boolean values to {0,1} numeric\n", "data_experiment['df'].v0 = data_experiment['df'].v0.astype(int)\n", "print(data_experiment['df'])\n", "model_experiment = CausalModel(data=data_experiment[\"df\"], \n", " treatment=data_experiment[\"treatment_name\"], outcome=data_experiment[\"outcome_name\"], \n", " graph=data_experiment[\"gml_graph\"])\n", "identified_estimand_experiment = model_experiment.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.ensemble import RandomForestRegressor\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'models': RandomForestRegressor()\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Avoiding retraining the estimator " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once an estimator is fitted, it can be reused to estimate effect on different data points. In this case, you can pass `fit_estimator=False` to `estimate_effect`. This works for any EconML estimator. We show an example for the T-learner below." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# For metalearners, need to provide all the features (except treatmeant and outcome)\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " fit_estimator=False,\n", " target_units=data_experiment[\"df\"].drop([\"v0\",\"y\", \"Z0\", \"Z1\"], axis=1)[9995:], \n", " method_params={})\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"random_common_cause\")\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"linear\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\",\n", " num_simulations=10 # at least 100 is good, setting to 10 for speed \n", " ) \n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.8,\n", " num_simulations=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More refutation methods to come, especially specific to the CATE estimators." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

andresmor-ms

11c4e0dafd6e824eb81ad14262457d954ae61468

affe0952f4aba6845247355c171565510c2c1673

Changed import.

andresmor-ms

py-why/dowhy

Functional api/causal estimators

* Introduce `fit()` method to estimators. * Refactor constructors to avoid using `*args` and `**kwargs` and have more explicit parameters. * Refactor refuters and other parts of the code to use `fit()` and modify arguments to `estimate_effect()`

2022-11-04 16:15:39+00:00

2022-12-03 17:07:53+00:00

docs/source/example_notebooks/dowhy-conditional-treatment-effects.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Conditional Average Treatment Effects (CATE) with DoWhy and EconML\n", "\n", "This is an experimental feature where we use [EconML](https://github.com/microsoft/econml) methods from DoWhy. Using EconML allows CATE estimation using different methods. \n", "\n", "All four steps of causal inference in DoWhy remain the same: model, identify, estimate, and refute. The key difference is that we now call econml methods in the estimation step. There is also a simpler example using linear regression to understand the intuition behind CATE estimators. \n", "\n", "All datasets are generated using linear structural equations.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import logging\n", "\n", "import dowhy\n", "from dowhy import CausalModel\n", "import dowhy.datasets\n", "\n", "import econml\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "BETA = 10" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " num_treatments=1,\n", " treatment_is_binary=False,\n", " num_discrete_common_causes=2,\n", " num_discrete_effect_modifiers=0,\n", " one_hot_encode=False)\n", "df=data['df']\n", "print(df.head())\n", "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = CausalModel(data=data[\"df\"], \n", " treatment=data[\"treatment_name\"], outcome=data[\"outcome_name\"], \n", " graph=data[\"gml_graph\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "identified_estimand= model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Model \n", "First, let us build some intuition using a linear model for estimating CATE. The effect modifiers (that lead to a heterogeneous treatment effect) can be modeled as interaction terms with the treatment. Thus, their value modulates the effect of treatment. \n", "\n", "Below the estimated effect of changing treatment from 0 to 1. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "linear_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.linear_regression\",\n", " control_value=0,\n", " treatment_value=1)\n", "print(linear_estimate) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## EconML methods\n", "We now move to the more advanced methods from the EconML package for estimating CATE.\n", "\n", "First, let us look at the double machine learning estimator. Method_name corresponds to the fully qualified name of the class that we want to use. For double ML, it is \"econml.dml.DML\". \n", "\n", "Target units defines the units over which the causal estimate is to be computed. This can be a lambda function filter on the original dataframe, a new Pandas dataframe, or a string corresponding to the three main kinds of target units (\"ate\", \"att\" and \"atc\"). Below we show an example of a lambda function. \n", "\n", "Method_params are passed directly to EconML. For details on allowed parameters, refer to the EconML documentation. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = lambda df: df[\"X0\"]>1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=False)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = 1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### CATE Object and Confidence Intervals\n", "EconML provides its own methods to compute confidence intervals. Using BootstrapInference in the example below. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "from econml.inference import BootstrapInference\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = \"ate\",\n", " confidence_intervals=True,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\": LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{\n", " 'inference': BootstrapInference(n_bootstrap_samples=100, n_jobs=-1),\n", " }\n", " })\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can provide a new inputs as target units and estimate CATE on them." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "test_cols= data['effect_modifier_names'] # only need effect modifiers' values\n", "test_arr = [np.random.uniform(0,1, 10) for _ in range(len(test_cols))] # all variables are sampled uniformly, sample of 10\n", "test_df = pd.DataFrame(np.array(test_arr).transpose(), columns=test_cols)\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = test_df,\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}\n", " })\n", "print(dml_estimate.cate_estimates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can also retrieve the raw EconML estimator object for any further operations" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dml_estimate._estimator_object)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Works with any EconML method\n", "In addition to double machine learning, below we example analyses using orthogonal forests, DRLearner (bug to fix), and neural network-based instrumental variables. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Binary treatment, Binary outcome" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_binary = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " treatment_is_binary=True, outcome_is_binary=True)\n", "# convert boolean values to {0,1} numeric\n", "data_binary['df'].v0 = data_binary['df'].v0.astype(int)\n", "data_binary['df'].y = data_binary['df'].y.astype(int)\n", "print(data_binary['df'])\n", "\n", "model_binary = CausalModel(data=data_binary[\"df\"], \n", " treatment=data_binary[\"treatment_name\"], outcome=data_binary[\"outcome_name\"], \n", " graph=data_binary[\"gml_graph\"])\n", "identified_estimand_binary = model_binary.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using DRLearner estimator" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LogisticRegressionCV\n", "#todo needs binary y\n", "drlearner_estimate = model_binary.estimate_effect(identified_estimand_binary, \n", " method_name=\"backdoor.econml.drlearner.LinearDRLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'model_propensity': LogisticRegressionCV(cv=3, solver='lbfgs', multi_class='auto')\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(drlearner_estimate)\n", "print(\"True causal estimate is\", data_binary[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Instrumental Variable Method" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import keras\n", "from econml.deepiv import DeepIVEstimator\n", "dims_zx = len(model.get_instruments())+len(model.get_effect_modifiers())\n", "dims_tx = len(model._treatment)+len(model.get_effect_modifiers())\n", "treatment_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_zx,)), # sum of dims of Z and X \n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17)]) \n", "response_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_tx,)), # sum of dims of T and X\n", " keras.layers.Dropout(0.17), \n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(1)])\n", "\n", "deepiv_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"iv.econml.deepiv.DeepIV\",\n", " target_units = lambda df: df[\"X0\"]>-1, \n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'n_components': 10, # Number of gaussians in the mixture density networks\n", " 'm': lambda z, x: treatment_model(keras.layers.concatenate([z, x])), # Treatment model,\n", " \"h\": lambda t, x: response_model(keras.layers.concatenate([t, x])), # Response model\n", " 'n_samples': 1, # Number of samples used to estimate the response\n", " 'first_stage_options': {'epochs':25},\n", " 'second_stage_options': {'epochs':25}\n", " },\n", " \"fit_params\":{}})\n", "print(deepiv_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metalearners" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_experiment = dowhy.datasets.linear_dataset(BETA, num_common_causes=5, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=5,\n", " treatment_is_binary=True, outcome_is_binary=False)\n", "# convert boolean values to {0,1} numeric\n", "data_experiment['df'].v0 = data_experiment['df'].v0.astype(int)\n", "print(data_experiment['df'])\n", "model_experiment = CausalModel(data=data_experiment[\"df\"], \n", " treatment=data_experiment[\"treatment_name\"], outcome=data_experiment[\"outcome_name\"], \n", " graph=data_experiment[\"gml_graph\"])\n", "identified_estimand_experiment = model_experiment.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.ensemble import RandomForestRegressor\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'models': RandomForestRegressor()\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Avoiding retraining the estimator " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once an estimator is fitted, it can be reused to estimate effect on different data points. In this case, you can pass `fit_estimator=False` to `estimate_effect`. This works for any EconML estimator. We show an example for the T-learner below." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# For metalearners, need to provide all the features (except treatmeant and outcome)\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " fit_estimator=False,\n", " target_units=data_experiment[\"df\"].drop([\"v0\",\"y\", \"Z0\", \"Z1\"], axis=1)[9995:], \n", " method_params={})\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"random_common_cause\")\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"linear\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\",\n", " num_simulations=10 # at least 100 is good, setting to 10 for speed \n", " ) \n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.8,\n", " num_simulations=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More refutation methods to come, especially specific to the CATE estimators." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.12" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Conditional Average Treatment Effects (CATE) with DoWhy and EconML\n", "\n", "This is an experimental feature where we use [EconML](https://github.com/microsoft/econml) methods from DoWhy. Using EconML allows CATE estimation using different methods. \n", "\n", "All four steps of causal inference in DoWhy remain the same: model, identify, estimate, and refute. The key difference is that we now call econml methods in the estimation step. There is also a simpler example using linear regression to understand the intuition behind CATE estimators. \n", "\n", "All datasets are generated using linear structural equations.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import logging\n", "\n", "import dowhy\n", "from dowhy import CausalModel\n", "import dowhy.datasets\n", "\n", "import econml\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "BETA = 10" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " num_treatments=1,\n", " treatment_is_binary=False,\n", " num_discrete_common_causes=2,\n", " num_discrete_effect_modifiers=0,\n", " one_hot_encode=False)\n", "df=data['df']\n", "print(df.head())\n", "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = CausalModel(data=data[\"df\"], \n", " treatment=data[\"treatment_name\"], outcome=data[\"outcome_name\"], \n", " graph=data[\"gml_graph\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "identified_estimand= model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Model \n", "First, let us build some intuition using a linear model for estimating CATE. The effect modifiers (that lead to a heterogeneous treatment effect) can be modeled as interaction terms with the treatment. Thus, their value modulates the effect of treatment. \n", "\n", "Below the estimated effect of changing treatment from 0 to 1. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "linear_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.linear_regression\",\n", " control_value=0,\n", " treatment_value=1)\n", "print(linear_estimate) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## EconML methods\n", "We now move to the more advanced methods from the EconML package for estimating CATE.\n", "\n", "First, let us look at the double machine learning estimator. Method_name corresponds to the fully qualified name of the class that we want to use. For double ML, it is \"econml.dml.DML\". \n", "\n", "Target units defines the units over which the causal estimate is to be computed. This can be a lambda function filter on the original dataframe, a new Pandas dataframe, or a string corresponding to the three main kinds of target units (\"ate\", \"att\" and \"atc\"). Below we show an example of a lambda function. \n", "\n", "Method_params are passed directly to EconML. For details on allowed parameters, refer to the EconML documentation. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = lambda df: df[\"X0\"]>1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=False)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(\"True causal estimate is\", data[\"ate\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dml_estimate = model.estimate_effect(identified_estimand, method_name=\"backdoor.econml.dml.DML\",\n", " control_value = 0,\n", " treatment_value = 1,\n", " target_units = 1, # condition used for CATE\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}})\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### CATE Object and Confidence Intervals\n", "EconML provides its own methods to compute confidence intervals. Using BootstrapInference in the example below. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "from econml.inference import BootstrapInference\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = \"ate\",\n", " confidence_intervals=True,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\": LassoCV(fit_intercept=False), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{\n", " 'inference': BootstrapInference(n_bootstrap_samples=100, n_jobs=-1),\n", " }\n", " })\n", "print(dml_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can provide a new inputs as target units and estimate CATE on them." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "test_cols= data['effect_modifier_names'] # only need effect modifiers' values\n", "test_arr = [np.random.uniform(0,1, 10) for _ in range(len(test_cols))] # all variables are sampled uniformly, sample of 10\n", "test_df = pd.DataFrame(np.array(test_arr).transpose(), columns=test_cols)\n", "dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.DML\",\n", " target_units = test_df,\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " \"model_final\":LassoCV(), \n", " 'featurizer':PolynomialFeatures(degree=1, include_bias=True)},\n", " \"fit_params\":{}\n", " })\n", "print(dml_estimate.cate_estimates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Can also retrieve the raw EconML estimator object for any further operations" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dml_estimate._estimator_object)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Works with any EconML method\n", "In addition to double machine learning, below we example analyses using orthogonal forests, DRLearner (bug to fix), and neural network-based instrumental variables. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Binary treatment, Binary outcome" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_binary = dowhy.datasets.linear_dataset(BETA, num_common_causes=4, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=2,\n", " treatment_is_binary=True, outcome_is_binary=True)\n", "# convert boolean values to {0,1} numeric\n", "data_binary['df'].v0 = data_binary['df'].v0.astype(int)\n", "data_binary['df'].y = data_binary['df'].y.astype(int)\n", "print(data_binary['df'])\n", "\n", "model_binary = CausalModel(data=data_binary[\"df\"], \n", " treatment=data_binary[\"treatment_name\"], outcome=data_binary[\"outcome_name\"], \n", " graph=data_binary[\"gml_graph\"])\n", "identified_estimand_binary = model_binary.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using DRLearner estimator" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LogisticRegressionCV\n", "#todo needs binary y\n", "drlearner_estimate = model_binary.estimate_effect(identified_estimand_binary, \n", " method_name=\"backdoor.econml.dr.LinearDRLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'model_propensity': LogisticRegressionCV(cv=3, solver='lbfgs', multi_class='auto')\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(drlearner_estimate)\n", "print(\"True causal estimate is\", data_binary[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Instrumental Variable Method" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import keras\n", "dims_zx = len(model.get_instruments())+len(model.get_effect_modifiers())\n", "dims_tx = len(model._treatment)+len(model.get_effect_modifiers())\n", "treatment_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_zx,)), # sum of dims of Z and X \n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17)]) \n", "response_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(dims_tx,)), # sum of dims of T and X\n", " keras.layers.Dropout(0.17), \n", " keras.layers.Dense(64, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(32, activation='relu'),\n", " keras.layers.Dropout(0.17),\n", " keras.layers.Dense(1)])\n", "\n", "deepiv_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"iv.econml.iv.nnet.DeepIV\",\n", " target_units = lambda df: df[\"X0\"]>-1, \n", " confidence_intervals=False,\n", " method_params={\"init_params\":{'n_components': 10, # Number of gaussians in the mixture density networks\n", " 'm': lambda z, x: treatment_model(keras.layers.concatenate([z, x])), # Treatment model,\n", " \"h\": lambda t, x: response_model(keras.layers.concatenate([t, x])), # Response model\n", " 'n_samples': 1, # Number of samples used to estimate the response\n", " 'first_stage_options': {'epochs':25},\n", " 'second_stage_options': {'epochs':25}\n", " },\n", " \"fit_params\":{}})\n", "print(deepiv_estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metalearners" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data_experiment = dowhy.datasets.linear_dataset(BETA, num_common_causes=5, num_samples=10000,\n", " num_instruments=2, num_effect_modifiers=5,\n", " treatment_is_binary=True, outcome_is_binary=False)\n", "# convert boolean values to {0,1} numeric\n", "data_experiment['df'].v0 = data_experiment['df'].v0.astype(int)\n", "print(data_experiment['df'])\n", "model_experiment = CausalModel(data=data_experiment[\"df\"], \n", " treatment=data_experiment[\"treatment_name\"], outcome=data_experiment[\"outcome_name\"], \n", " graph=data_experiment[\"gml_graph\"])\n", "identified_estimand_experiment = model_experiment.identify_effect(proceed_when_unidentifiable=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sklearn.ensemble import RandomForestRegressor\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " method_params={\"init_params\":{\n", " 'models': RandomForestRegressor()\n", " },\n", " \"fit_params\":{}\n", " })\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Avoiding retraining the estimator " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once an estimator is fitted, it can be reused to estimate effect on different data points. In this case, you can pass `fit_estimator=False` to `estimate_effect`. This works for any EconML estimator. We show an example for the T-learner below." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# For metalearners, need to provide all the features (except treatmeant and outcome)\n", "metalearner_estimate = model_experiment.estimate_effect(identified_estimand_experiment, \n", " method_name=\"backdoor.econml.metalearners.TLearner\",\n", " confidence_intervals=False,\n", " fit_estimator=False,\n", " target_units=data_experiment[\"df\"].drop([\"v0\",\"y\", \"Z0\", \"Z1\"], axis=1)[9995:], \n", " method_params={})\n", "print(metalearner_estimate)\n", "print(\"True causal estimate is\", data_experiment[\"ate\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refuting the estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a random common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_random=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"random_common_cause\")\n", "print(res_random)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding an unobserved common cause variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unobserved=model.refute_estimate(identified_estimand, dml_estimate, method_name=\"add_unobserved_common_cause\",\n", " confounders_effect_on_treatment=\"linear\", confounders_effect_on_outcome=\"linear\",\n", " effect_strength_on_treatment=0.01, effect_strength_on_outcome=0.02)\n", "print(res_unobserved)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replacing treatment with a random (placebo) variable" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_placebo=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\",\n", " num_simulations=10 # at least 100 is good, setting to 10 for speed \n", " ) \n", "print(res_placebo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Removing a random subset of the data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_subset=model.refute_estimate(identified_estimand, dml_estimate,\n", " method_name=\"data_subset_refuter\", subset_fraction=0.8,\n", " num_simulations=10)\n", "print(res_subset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More refutation methods to come, especially specific to the CATE estimators." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

andresmor-ms

11c4e0dafd6e824eb81ad14262457d954ae61468

affe0952f4aba6845247355c171565510c2c1673

This is not needed, only need to specify the correct method_name parameter

andresmor-ms

py-why/dowhy

Functional api/causal estimators

* Introduce `fit()` method to estimators. * Refactor constructors to avoid using `*args` and `**kwargs` and have more explicit parameters. * Refactor refuters and other parts of the code to use `fit()` and modify arguments to `estimate_effect()`

2022-11-04 16:15:39+00:00

2022-12-03 17:07:53+00:00

docs/source/example_notebooks/dowhy_functional_api.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Functional API Preview\n", "\n", "This notebook is part of a set of notebooks that provides a preview of the proposed functional API for dowhy. For details on the new API for DoWhy, check out https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 It is a work-in-progress and is updated as we add new functionality. We welcome your feedback through Discord or on the Discussions page.\n", "This functional API is designed with backwards compatibility. So both the old and new API will continue to co-exist and work for the immediate new releases. Gradually the old API using CausalModel will be deprecated in favor of the new API. \n", "\n", "The current Functional API covers:\n", "* Identify Effect:\n", " * `identify_effect(...)`: Run the identify effect algorithm using defaults just provide the graph, treatment and outcome.\n", " * `auto_identify_effect(...)`: More configurable version of `identify_effect(...)`.\n", " * `id_identify_effect(...)`: Identify Effect using the ID-Algorithm.\n", "* Refute Estimate:\n", " * `refute_estimate`: Function to run a set of the refuters below with the default parameters.\n", " * `refute_bootstrap`: Refute an estimate by running it on a random sample of the data containing measurement error in the confounders.\n", " * `refute_data_subset`: Refute an estimate by rerunning it on a random subset of the original data.\n", " * `refute_random_common_cause`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved).\n", " * `refute_placebo_treatment`: Refute an estimate by replacing treatment with a randomly-generated placebo variable.\n", " * `sensitivity_simulation`: Add an unobserved confounder for refutation (Simulation of an unobserved confounder).\n", " * `sensitivity_linear_partial_r2`: Add an unobserved confounder for refutation (Linear partial R2 : Sensitivity Analysis for linear models).\n", " * `sensitivity_non_parametric_partial_r2`: Add an unobserved confounder for refutation (Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models).\n", " * `sensitivity_e_value`: Computes E-value for point estimate and confidence limits. Benchmarks E-values against measured confounders using Observed Covariate E-values. Plots E-values and Observed\n", " Covariate E-values.\n", " * `refute_dummy_outcome`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import Dependencies" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Functional API imports\n", "from dowhy.causal_identifier import (\n", " BackdoorAdjustment,\n", " EstimandType,\n", " identify_effect,\n", " identify_effect_auto,\n", " identify_effect_id,\n", ") # import effect identifier\n", "from dowhy.causal_refuters import (\n", " refute_bootstrap,\n", " refute_data_subset,\n", " refute_random_common_cause,\n", " refute_placebo_treatment,\n", " sensitivity_e_value,\n", " sensitivity_linear_partial_r2,\n", " sensitivity_non_parametric_partial_r2,\n", " sensitivity_simulation,\n", " refute_dummy_outcome,\n", " refute_estimate,\n", ") # import refuters\n", "\n", "from dowhy.causal_estimators.propensity_score_matching_estimator import PropensityScoreMatchingEstimator\n", "\n", "from dowhy.utils.api import parse_state\n", "\n", "from dowhy.causal_estimator import estimate_effect # Estimate effect function\n", "\n", "from dowhy.causal_graph import CausalGraph\n", "\n", "# Other imports required\n", "from dowhy.datasets import linear_dataset\n", "from dowhy import CausalModel # We still need this as we haven't created the functional API for effect estimation\n", "import econml\n", "\n", "# Config dict to set the logging level\n", "import logging.config\n", "\n", "DEFAULT_LOGGING = {\n", " \"version\": 1,\n", " \"disable_existing_loggers\": False,\n", " \"loggers\": {\n", " \"\": {\n", " \"level\": \"WARN\",\n", " },\n", " },\n", "}\n", "\n", "\n", "# set random seed for deterministic dataset generation \n", "# and avoid problems when running tests\n", "import numpy as np\n", "np.random.seed(1)\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "# Disabling warnings output\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "\n", "warnings.filterwarnings(action=\"ignore\", category=DataConversionWarning)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create the Datasets" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Parameters for creating the Dataset\n", "TREATMENT_IS_BINARY = True\n", "BETA = 10\n", "NUM_SAMPLES = 500\n", "NUM_CONFOUNDERS = 3\n", "NUM_INSTRUMENTS = 2\n", "NUM_EFFECT_MODIFIERS = 2\n", "\n", "# Creating a Linear Dataset with the given parameters\n", "data = linear_dataset(\n", " beta=BETA,\n", " num_common_causes=NUM_CONFOUNDERS,\n", " num_instruments=NUM_INSTRUMENTS,\n", " num_effect_modifiers=NUM_EFFECT_MODIFIERS,\n", " num_samples=NUM_SAMPLES,\n", " treatment_is_binary=True,\n", ")\n", "\n", "treatment_name = data[\"treatment_name\"]\n", "print(treatment_name)\n", "outcome_name = data[\"outcome_name\"]\n", "print(outcome_name)\n", "\n", "graph = CausalGraph(\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " graph=data[\"gml_graph\"],\n", " effect_modifier_names=data[\"effect_modifier_names\"],\n", " common_cause_names=data[\"common_causes_names\"],\n", " observed_node_names=data[\"df\"].columns.tolist(),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Default identify_effect call example:\n", "identified_estimand = identify_effect(graph, treatment_name, outcome_name)\n", "\n", "# auto_identify_effect example with extra parameters:\n", "identified_estimand_auto = identify_effect_auto(\n", " graph,\n", " treatment_name,\n", " outcome_name,\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_EFFICIENT,\n", ")\n", "\n", "# id_identify_effect example:\n", "identified_estimand_id = identify_effect_id(\n", " graph, treatment_name, outcome_name\n", ") # Note that the return type for id_identify_effect is IDExpression and not IdentifiedEstimand\n", "\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Basic Estimate Effect function\n", "\n", "\n", "propensity_score_estimator = PropensityScoreMatchingEstimator(\n", " data=data[\"df\"],\n", " identified_estimand=identified_estimand,\n", " treatment=treatment_name,\n", " outcome=outcome_name,\n", " control_value=0,\n", " treatment_value=1,\n", " test_significance=None,\n", " evaluate_effect_strength=False,\n", " confidence_intervals=False,\n", " target_units=\"ate\",\n", " effect_modifiers=graph.get_effect_modifiers(treatment_name, outcome_name),\n", ")\n", "\n", "estimate = estimate_effect(\n", " treatment=treatment_name,\n", " outcome=outcome_name,\n", " identified_estimand=identified_estimand,\n", " identifier_name=\"backdoor\",\n", " method=propensity_score_estimator,\n", ")\n", "\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# You can call the refute_estimate function for executing several refuters using default parameters\n", "# Currently this function does not support sensitivity_* functions\n", "refutation_results = refute_estimate(\n", " data[\"df\"],\n", " identified_estimand,\n", " estimate,\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " refuters=[refute_bootstrap, refute_data_subset],\n", ")\n", "\n", "for result in refutation_results:\n", " print(result)\n", "\n", "# Or you can execute refute methods directly\n", "# You can change the refute_bootstrap - refute_data_subset for any of the other refuters and add the missing parameters\n", "\n", "bootstrap_refutation = refute_bootstrap(data[\"df\"], identified_estimand, estimate)\n", "print(bootstrap_refutation)\n", "\n", "data_subset_refutation = refute_data_subset(data[\"df\"], identified_estimand, estimate)\n", "print(data_subset_refutation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Backwards Compatibility\n", "\n", "This section shows replicating the same results using only the CausalModel API" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create Causal Model\n", "causal_model = CausalModel(data=data[\"df\"], treatment=treatment_name, outcome=outcome_name, graph=data[\"gml_graph\"])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand_causal_model_api = (\n", " causal_model.identify_effect()\n", ") # graph, treatment and outcome comes from the causal_model object\n", "\n", "print(identified_estimand_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate_causal_model_api = causal_model.estimate_effect(\n", " identified_estimand_causal_model_api, method_name=\"backdoor.propensity_score_matching\"\n", ")\n", "\n", "print(estimate_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bootstrap_refutation_causal_model_api = causal_model.refute_estimate(identified_estimand_causal_model_api, estimate_causal_model_api, \"bootstrap_refuter\")\n", "print(bootstrap_refutation_causal_model_api)\n", "\n", "data_subset_refutation_causal_model_api = causal_model.refute_estimate(\n", " identified_estimand_causal_model_api, estimate_causal_model_api, \"data_subset_refuter\"\n", ")\n", "\n", "print(data_subset_refutation_causal_model_api)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Functional API Preview\n", "\n", "This notebook is part of a set of notebooks that provides a preview of the proposed functional API for dowhy. For details on the new API for DoWhy, check out https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 It is a work-in-progress and is updated as we add new functionality. We welcome your feedback through Discord or on the Discussions page.\n", "This functional API is designed with backwards compatibility. So both the old and new API will continue to co-exist and work for the immediate new releases. Gradually the old API using CausalModel will be deprecated in favor of the new API. \n", "\n", "The current Functional API covers:\n", "* Identify Effect:\n", " * `identify_effect(...)`: Run the identify effect algorithm using defaults just provide the graph, treatment and outcome.\n", " * `auto_identify_effect(...)`: More configurable version of `identify_effect(...)`.\n", " * `id_identify_effect(...)`: Identify Effect using the ID-Algorithm.\n", "* Refute Estimate:\n", " * `refute_estimate`: Function to run a set of the refuters below with the default parameters.\n", " * `refute_bootstrap`: Refute an estimate by running it on a random sample of the data containing measurement error in the confounders.\n", " * `refute_data_subset`: Refute an estimate by rerunning it on a random subset of the original data.\n", " * `refute_random_common_cause`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved).\n", " * `refute_placebo_treatment`: Refute an estimate by replacing treatment with a randomly-generated placebo variable.\n", " * `sensitivity_simulation`: Add an unobserved confounder for refutation (Simulation of an unobserved confounder).\n", " * `sensitivity_linear_partial_r2`: Add an unobserved confounder for refutation (Linear partial R2 : Sensitivity Analysis for linear models).\n", " * `sensitivity_non_parametric_partial_r2`: Add an unobserved confounder for refutation (Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models).\n", " * `sensitivity_e_value`: Computes E-value for point estimate and confidence limits. Benchmarks E-values against measured confounders using Observed Covariate E-values. Plots E-values and Observed\n", " Covariate E-values.\n", " * `refute_dummy_outcome`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import Dependencies" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Functional API imports\n", "from dowhy.causal_identifier import (\n", " BackdoorAdjustment,\n", " EstimandType,\n", " identify_effect,\n", " identify_effect_auto,\n", " identify_effect_id,\n", ") # import effect identifier\n", "from dowhy.causal_refuters import (\n", " refute_bootstrap,\n", " refute_data_subset,\n", " refute_random_common_cause,\n", " refute_placebo_treatment,\n", " sensitivity_e_value,\n", " sensitivity_linear_partial_r2,\n", " sensitivity_non_parametric_partial_r2,\n", " sensitivity_simulation,\n", " refute_dummy_outcome,\n", " refute_estimate,\n", ") # import refuters\n", "\n", "from dowhy.causal_estimators.propensity_score_matching_estimator import PropensityScoreMatchingEstimator\n", "from dowhy.causal_estimators.econml import Econml\n", "\n", "from dowhy.utils.api import parse_state\n", "\n", "from dowhy.causal_estimator import estimate_effect # Estimate effect function\n", "\n", "from dowhy.causal_graph import CausalGraph\n", "\n", "# Other imports required\n", "from dowhy.datasets import linear_dataset\n", "from dowhy import CausalModel # We still need this as we haven't created the functional API for effect estimation\n", "import econml\n", "\n", "# Config dict to set the logging level\n", "import logging.config\n", "\n", "DEFAULT_LOGGING = {\n", " \"version\": 1,\n", " \"disable_existing_loggers\": False,\n", " \"loggers\": {\n", " \"\": {\n", " \"level\": \"WARN\",\n", " },\n", " },\n", "}\n", "\n", "\n", "# set random seed for deterministic dataset generation \n", "# and avoid problems when running tests\n", "import numpy as np\n", "np.random.seed(1)\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "# Disabling warnings output\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "\n", "warnings.filterwarnings(action=\"ignore\", category=DataConversionWarning)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create the Datasets" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Parameters for creating the Dataset\n", "TREATMENT_IS_BINARY = True\n", "BETA = 10\n", "NUM_SAMPLES = 500\n", "NUM_CONFOUNDERS = 3\n", "NUM_INSTRUMENTS = 2\n", "NUM_EFFECT_MODIFIERS = 2\n", "\n", "# Creating a Linear Dataset with the given parameters\n", "data = linear_dataset(\n", " beta=BETA,\n", " num_common_causes=NUM_CONFOUNDERS,\n", " num_instruments=NUM_INSTRUMENTS,\n", " num_effect_modifiers=NUM_EFFECT_MODIFIERS,\n", " num_samples=NUM_SAMPLES,\n", " treatment_is_binary=True,\n", ")\n", "\n", "data_2 = linear_dataset(\n", " beta=BETA,\n", " num_common_causes=NUM_CONFOUNDERS,\n", " num_instruments=NUM_INSTRUMENTS,\n", " num_effect_modifiers=NUM_EFFECT_MODIFIERS,\n", " num_samples=NUM_SAMPLES,\n", " treatment_is_binary=True,\n", ")\n", "\n", "treatment_name = data[\"treatment_name\"]\n", "print(treatment_name)\n", "outcome_name = data[\"outcome_name\"]\n", "print(outcome_name)\n", "\n", "graph = CausalGraph(\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " graph=data[\"gml_graph\"],\n", " effect_modifier_names=data[\"effect_modifier_names\"],\n", " common_cause_names=data[\"common_causes_names\"],\n", " observed_node_names=data[\"df\"].columns.tolist(),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Default identify_effect call example:\n", "identified_estimand = identify_effect(graph, treatment_name, outcome_name)\n", "\n", "# auto_identify_effect example with extra parameters:\n", "identified_estimand_auto = identify_effect_auto(\n", " graph,\n", " treatment_name,\n", " outcome_name,\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_EFFICIENT,\n", ")\n", "\n", "# id_identify_effect example:\n", "identified_estimand_id = identify_effect_id(\n", " graph, treatment_name, outcome_name\n", ") # Note that the return type for id_identify_effect is IDExpression and not IdentifiedEstimand\n", "\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Basic Estimate Effect function\n", "estimator = PropensityScoreMatchingEstimator(\n", " identified_estimand=identified_estimand,\n", " test_significance=None,\n", " evaluate_effect_strength=False,\n", " confidence_intervals=False,\n", ").fit(\n", " data=data[\"df\"],\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " effect_modifier_names=graph.get_effect_modifiers(treatment_name, outcome_name),\n", ")\n", "\n", "estimate = estimator.estimate_effect(\n", " control_value=0,\n", " treatment_value=1,\n", " target_units=\"ate\",\n", ")\n", "\n", "# Using same estimator with different data\n", "second_estimate = estimator.estimate_effect(\n", " data=data_2[\"df\"],\n", " control_value=0,\n", " treatment_value=1,\n", " target_units=\"ate\",\n", ")\n", "\n", "print(estimate)\n", "print(\"-----------\")\n", "print(second_estimate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# EconML estimator example\n", "from econml.dml import DML\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.preprocessing import PolynomialFeatures\n", "\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "\n", "estimator = Econml(\n", " identified_estimand=identified_estimand,\n", " econml_estimator=DML(\n", " model_y=GradientBoostingRegressor(),\n", " model_t=GradientBoostingRegressor(),\n", " model_final=LassoCV(fit_intercept=False),\n", " featurizer=PolynomialFeatures(degree=1, include_bias=True),\n", " ),\n", ").fit(\n", " data=data[\"df\"],\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " effect_modifier_names=graph.get_effect_modifiers(treatment_name, outcome_name),\n", ")\n", "\n", "estimate_econml = estimator.estimate_effect(\n", " control_value=0,\n", " treatment_value=1,\n", " target_units=\"ate\",\n", ")\n", "\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# You can call the refute_estimate function for executing several refuters using default parameters\n", "# Currently this function does not support sensitivity_* functions\n", "refutation_results = refute_estimate(\n", " data[\"df\"],\n", " identified_estimand,\n", " estimate,\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " refuters=[refute_bootstrap, refute_data_subset],\n", ")\n", "\n", "for result in refutation_results:\n", " print(result)\n", "\n", "# Or you can execute refute methods directly\n", "# You can change the refute_bootstrap - refute_data_subset for any of the other refuters and add the missing parameters\n", "\n", "bootstrap_refutation = refute_bootstrap(data[\"df\"], identified_estimand, estimate)\n", "print(bootstrap_refutation)\n", "\n", "data_subset_refutation = refute_data_subset(data[\"df\"], identified_estimand, estimate)\n", "print(data_subset_refutation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Backwards Compatibility\n", "\n", "This section shows replicating the same results using only the CausalModel API" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create Causal Model\n", "causal_model = CausalModel(data=data[\"df\"], treatment=treatment_name, outcome=outcome_name, graph=data[\"gml_graph\"])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand_causal_model_api = (\n", " causal_model.identify_effect()\n", ") # graph, treatment and outcome comes from the causal_model object\n", "\n", "print(identified_estimand_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate_causal_model_api = causal_model.estimate_effect(\n", " identified_estimand_causal_model_api, method_name=\"backdoor.propensity_score_matching\"\n", ")\n", "\n", "print(estimate_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bootstrap_refutation_causal_model_api = causal_model.refute_estimate(identified_estimand_causal_model_api, estimate_causal_model_api, \"bootstrap_refuter\")\n", "print(bootstrap_refutation_causal_model_api)\n", "\n", "data_subset_refutation_causal_model_api = causal_model.refute_estimate(\n", " identified_estimand_causal_model_api, estimate_causal_model_api, \"data_subset_refuter\"\n", ")\n", "\n", "print(data_subset_refutation_causal_model_api)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

andresmor-ms

11c4e0dafd6e824eb81ad14262457d954ae61468

affe0952f4aba6845247355c171565510c2c1673

can you also add an example where estimate_effect is called again for a different (test) dataset?

amit-sharma

py-why/dowhy

Functional api/causal estimators

* Introduce `fit()` method to estimators. * Refactor constructors to avoid using `*args` and `**kwargs` and have more explicit parameters. * Refactor refuters and other parts of the code to use `fit()` and modify arguments to `estimate_effect()`

2022-11-04 16:15:39+00:00

2022-12-03 17:07:53+00:00

docs/source/example_notebooks/dowhy_functional_api.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Functional API Preview\n", "\n", "This notebook is part of a set of notebooks that provides a preview of the proposed functional API for dowhy. For details on the new API for DoWhy, check out https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 It is a work-in-progress and is updated as we add new functionality. We welcome your feedback through Discord or on the Discussions page.\n", "This functional API is designed with backwards compatibility. So both the old and new API will continue to co-exist and work for the immediate new releases. Gradually the old API using CausalModel will be deprecated in favor of the new API. \n", "\n", "The current Functional API covers:\n", "* Identify Effect:\n", " * `identify_effect(...)`: Run the identify effect algorithm using defaults just provide the graph, treatment and outcome.\n", " * `auto_identify_effect(...)`: More configurable version of `identify_effect(...)`.\n", " * `id_identify_effect(...)`: Identify Effect using the ID-Algorithm.\n", "* Refute Estimate:\n", " * `refute_estimate`: Function to run a set of the refuters below with the default parameters.\n", " * `refute_bootstrap`: Refute an estimate by running it on a random sample of the data containing measurement error in the confounders.\n", " * `refute_data_subset`: Refute an estimate by rerunning it on a random subset of the original data.\n", " * `refute_random_common_cause`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved).\n", " * `refute_placebo_treatment`: Refute an estimate by replacing treatment with a randomly-generated placebo variable.\n", " * `sensitivity_simulation`: Add an unobserved confounder for refutation (Simulation of an unobserved confounder).\n", " * `sensitivity_linear_partial_r2`: Add an unobserved confounder for refutation (Linear partial R2 : Sensitivity Analysis for linear models).\n", " * `sensitivity_non_parametric_partial_r2`: Add an unobserved confounder for refutation (Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models).\n", " * `sensitivity_e_value`: Computes E-value for point estimate and confidence limits. Benchmarks E-values against measured confounders using Observed Covariate E-values. Plots E-values and Observed\n", " Covariate E-values.\n", " * `refute_dummy_outcome`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import Dependencies" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Functional API imports\n", "from dowhy.causal_identifier import (\n", " BackdoorAdjustment,\n", " EstimandType,\n", " identify_effect,\n", " identify_effect_auto,\n", " identify_effect_id,\n", ") # import effect identifier\n", "from dowhy.causal_refuters import (\n", " refute_bootstrap,\n", " refute_data_subset,\n", " refute_random_common_cause,\n", " refute_placebo_treatment,\n", " sensitivity_e_value,\n", " sensitivity_linear_partial_r2,\n", " sensitivity_non_parametric_partial_r2,\n", " sensitivity_simulation,\n", " refute_dummy_outcome,\n", " refute_estimate,\n", ") # import refuters\n", "\n", "from dowhy.causal_estimators.propensity_score_matching_estimator import PropensityScoreMatchingEstimator\n", "\n", "from dowhy.utils.api import parse_state\n", "\n", "from dowhy.causal_estimator import estimate_effect # Estimate effect function\n", "\n", "from dowhy.causal_graph import CausalGraph\n", "\n", "# Other imports required\n", "from dowhy.datasets import linear_dataset\n", "from dowhy import CausalModel # We still need this as we haven't created the functional API for effect estimation\n", "import econml\n", "\n", "# Config dict to set the logging level\n", "import logging.config\n", "\n", "DEFAULT_LOGGING = {\n", " \"version\": 1,\n", " \"disable_existing_loggers\": False,\n", " \"loggers\": {\n", " \"\": {\n", " \"level\": \"WARN\",\n", " },\n", " },\n", "}\n", "\n", "\n", "# set random seed for deterministic dataset generation \n", "# and avoid problems when running tests\n", "import numpy as np\n", "np.random.seed(1)\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "# Disabling warnings output\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "\n", "warnings.filterwarnings(action=\"ignore\", category=DataConversionWarning)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create the Datasets" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Parameters for creating the Dataset\n", "TREATMENT_IS_BINARY = True\n", "BETA = 10\n", "NUM_SAMPLES = 500\n", "NUM_CONFOUNDERS = 3\n", "NUM_INSTRUMENTS = 2\n", "NUM_EFFECT_MODIFIERS = 2\n", "\n", "# Creating a Linear Dataset with the given parameters\n", "data = linear_dataset(\n", " beta=BETA,\n", " num_common_causes=NUM_CONFOUNDERS,\n", " num_instruments=NUM_INSTRUMENTS,\n", " num_effect_modifiers=NUM_EFFECT_MODIFIERS,\n", " num_samples=NUM_SAMPLES,\n", " treatment_is_binary=True,\n", ")\n", "\n", "treatment_name = data[\"treatment_name\"]\n", "print(treatment_name)\n", "outcome_name = data[\"outcome_name\"]\n", "print(outcome_name)\n", "\n", "graph = CausalGraph(\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " graph=data[\"gml_graph\"],\n", " effect_modifier_names=data[\"effect_modifier_names\"],\n", " common_cause_names=data[\"common_causes_names\"],\n", " observed_node_names=data[\"df\"].columns.tolist(),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Default identify_effect call example:\n", "identified_estimand = identify_effect(graph, treatment_name, outcome_name)\n", "\n", "# auto_identify_effect example with extra parameters:\n", "identified_estimand_auto = identify_effect_auto(\n", " graph,\n", " treatment_name,\n", " outcome_name,\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_EFFICIENT,\n", ")\n", "\n", "# id_identify_effect example:\n", "identified_estimand_id = identify_effect_id(\n", " graph, treatment_name, outcome_name\n", ") # Note that the return type for id_identify_effect is IDExpression and not IdentifiedEstimand\n", "\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Basic Estimate Effect function\n", "\n", "\n", "propensity_score_estimator = PropensityScoreMatchingEstimator(\n", " data=data[\"df\"],\n", " identified_estimand=identified_estimand,\n", " treatment=treatment_name,\n", " outcome=outcome_name,\n", " control_value=0,\n", " treatment_value=1,\n", " test_significance=None,\n", " evaluate_effect_strength=False,\n", " confidence_intervals=False,\n", " target_units=\"ate\",\n", " effect_modifiers=graph.get_effect_modifiers(treatment_name, outcome_name),\n", ")\n", "\n", "estimate = estimate_effect(\n", " treatment=treatment_name,\n", " outcome=outcome_name,\n", " identified_estimand=identified_estimand,\n", " identifier_name=\"backdoor\",\n", " method=propensity_score_estimator,\n", ")\n", "\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# You can call the refute_estimate function for executing several refuters using default parameters\n", "# Currently this function does not support sensitivity_* functions\n", "refutation_results = refute_estimate(\n", " data[\"df\"],\n", " identified_estimand,\n", " estimate,\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " refuters=[refute_bootstrap, refute_data_subset],\n", ")\n", "\n", "for result in refutation_results:\n", " print(result)\n", "\n", "# Or you can execute refute methods directly\n", "# You can change the refute_bootstrap - refute_data_subset for any of the other refuters and add the missing parameters\n", "\n", "bootstrap_refutation = refute_bootstrap(data[\"df\"], identified_estimand, estimate)\n", "print(bootstrap_refutation)\n", "\n", "data_subset_refutation = refute_data_subset(data[\"df\"], identified_estimand, estimate)\n", "print(data_subset_refutation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Backwards Compatibility\n", "\n", "This section shows replicating the same results using only the CausalModel API" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create Causal Model\n", "causal_model = CausalModel(data=data[\"df\"], treatment=treatment_name, outcome=outcome_name, graph=data[\"gml_graph\"])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand_causal_model_api = (\n", " causal_model.identify_effect()\n", ") # graph, treatment and outcome comes from the causal_model object\n", "\n", "print(identified_estimand_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate_causal_model_api = causal_model.estimate_effect(\n", " identified_estimand_causal_model_api, method_name=\"backdoor.propensity_score_matching\"\n", ")\n", "\n", "print(estimate_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bootstrap_refutation_causal_model_api = causal_model.refute_estimate(identified_estimand_causal_model_api, estimate_causal_model_api, \"bootstrap_refuter\")\n", "print(bootstrap_refutation_causal_model_api)\n", "\n", "data_subset_refutation_causal_model_api = causal_model.refute_estimate(\n", " identified_estimand_causal_model_api, estimate_causal_model_api, \"data_subset_refuter\"\n", ")\n", "\n", "print(data_subset_refutation_causal_model_api)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Functional API Preview\n", "\n", "This notebook is part of a set of notebooks that provides a preview of the proposed functional API for dowhy. For details on the new API for DoWhy, check out https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 It is a work-in-progress and is updated as we add new functionality. We welcome your feedback through Discord or on the Discussions page.\n", "This functional API is designed with backwards compatibility. So both the old and new API will continue to co-exist and work for the immediate new releases. Gradually the old API using CausalModel will be deprecated in favor of the new API. \n", "\n", "The current Functional API covers:\n", "* Identify Effect:\n", " * `identify_effect(...)`: Run the identify effect algorithm using defaults just provide the graph, treatment and outcome.\n", " * `auto_identify_effect(...)`: More configurable version of `identify_effect(...)`.\n", " * `id_identify_effect(...)`: Identify Effect using the ID-Algorithm.\n", "* Refute Estimate:\n", " * `refute_estimate`: Function to run a set of the refuters below with the default parameters.\n", " * `refute_bootstrap`: Refute an estimate by running it on a random sample of the data containing measurement error in the confounders.\n", " * `refute_data_subset`: Refute an estimate by rerunning it on a random subset of the original data.\n", " * `refute_random_common_cause`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved).\n", " * `refute_placebo_treatment`: Refute an estimate by replacing treatment with a randomly-generated placebo variable.\n", " * `sensitivity_simulation`: Add an unobserved confounder for refutation (Simulation of an unobserved confounder).\n", " * `sensitivity_linear_partial_r2`: Add an unobserved confounder for refutation (Linear partial R2 : Sensitivity Analysis for linear models).\n", " * `sensitivity_non_parametric_partial_r2`: Add an unobserved confounder for refutation (Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models).\n", " * `sensitivity_e_value`: Computes E-value for point estimate and confidence limits. Benchmarks E-values against measured confounders using Observed Covariate E-values. Plots E-values and Observed\n", " Covariate E-values.\n", " * `refute_dummy_outcome`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import Dependencies" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Functional API imports\n", "from dowhy.causal_identifier import (\n", " BackdoorAdjustment,\n", " EstimandType,\n", " identify_effect,\n", " identify_effect_auto,\n", " identify_effect_id,\n", ") # import effect identifier\n", "from dowhy.causal_refuters import (\n", " refute_bootstrap,\n", " refute_data_subset,\n", " refute_random_common_cause,\n", " refute_placebo_treatment,\n", " sensitivity_e_value,\n", " sensitivity_linear_partial_r2,\n", " sensitivity_non_parametric_partial_r2,\n", " sensitivity_simulation,\n", " refute_dummy_outcome,\n", " refute_estimate,\n", ") # import refuters\n", "\n", "from dowhy.causal_estimators.propensity_score_matching_estimator import PropensityScoreMatchingEstimator\n", "from dowhy.causal_estimators.econml import Econml\n", "\n", "from dowhy.utils.api import parse_state\n", "\n", "from dowhy.causal_estimator import estimate_effect # Estimate effect function\n", "\n", "from dowhy.causal_graph import CausalGraph\n", "\n", "# Other imports required\n", "from dowhy.datasets import linear_dataset\n", "from dowhy import CausalModel # We still need this as we haven't created the functional API for effect estimation\n", "import econml\n", "\n", "# Config dict to set the logging level\n", "import logging.config\n", "\n", "DEFAULT_LOGGING = {\n", " \"version\": 1,\n", " \"disable_existing_loggers\": False,\n", " \"loggers\": {\n", " \"\": {\n", " \"level\": \"WARN\",\n", " },\n", " },\n", "}\n", "\n", "\n", "# set random seed for deterministic dataset generation \n", "# and avoid problems when running tests\n", "import numpy as np\n", "np.random.seed(1)\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "# Disabling warnings output\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "\n", "warnings.filterwarnings(action=\"ignore\", category=DataConversionWarning)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create the Datasets" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Parameters for creating the Dataset\n", "TREATMENT_IS_BINARY = True\n", "BETA = 10\n", "NUM_SAMPLES = 500\n", "NUM_CONFOUNDERS = 3\n", "NUM_INSTRUMENTS = 2\n", "NUM_EFFECT_MODIFIERS = 2\n", "\n", "# Creating a Linear Dataset with the given parameters\n", "data = linear_dataset(\n", " beta=BETA,\n", " num_common_causes=NUM_CONFOUNDERS,\n", " num_instruments=NUM_INSTRUMENTS,\n", " num_effect_modifiers=NUM_EFFECT_MODIFIERS,\n", " num_samples=NUM_SAMPLES,\n", " treatment_is_binary=True,\n", ")\n", "\n", "data_2 = linear_dataset(\n", " beta=BETA,\n", " num_common_causes=NUM_CONFOUNDERS,\n", " num_instruments=NUM_INSTRUMENTS,\n", " num_effect_modifiers=NUM_EFFECT_MODIFIERS,\n", " num_samples=NUM_SAMPLES,\n", " treatment_is_binary=True,\n", ")\n", "\n", "treatment_name = data[\"treatment_name\"]\n", "print(treatment_name)\n", "outcome_name = data[\"outcome_name\"]\n", "print(outcome_name)\n", "\n", "graph = CausalGraph(\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " graph=data[\"gml_graph\"],\n", " effect_modifier_names=data[\"effect_modifier_names\"],\n", " common_cause_names=data[\"common_causes_names\"],\n", " observed_node_names=data[\"df\"].columns.tolist(),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Default identify_effect call example:\n", "identified_estimand = identify_effect(graph, treatment_name, outcome_name)\n", "\n", "# auto_identify_effect example with extra parameters:\n", "identified_estimand_auto = identify_effect_auto(\n", " graph,\n", " treatment_name,\n", " outcome_name,\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_EFFICIENT,\n", ")\n", "\n", "# id_identify_effect example:\n", "identified_estimand_id = identify_effect_id(\n", " graph, treatment_name, outcome_name\n", ") # Note that the return type for id_identify_effect is IDExpression and not IdentifiedEstimand\n", "\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Basic Estimate Effect function\n", "estimator = PropensityScoreMatchingEstimator(\n", " identified_estimand=identified_estimand,\n", " test_significance=None,\n", " evaluate_effect_strength=False,\n", " confidence_intervals=False,\n", ").fit(\n", " data=data[\"df\"],\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " effect_modifier_names=graph.get_effect_modifiers(treatment_name, outcome_name),\n", ")\n", "\n", "estimate = estimator.estimate_effect(\n", " control_value=0,\n", " treatment_value=1,\n", " target_units=\"ate\",\n", ")\n", "\n", "# Using same estimator with different data\n", "second_estimate = estimator.estimate_effect(\n", " data=data_2[\"df\"],\n", " control_value=0,\n", " treatment_value=1,\n", " target_units=\"ate\",\n", ")\n", "\n", "print(estimate)\n", "print(\"-----------\")\n", "print(second_estimate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# EconML estimator example\n", "from econml.dml import DML\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.preprocessing import PolynomialFeatures\n", "\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "\n", "estimator = Econml(\n", " identified_estimand=identified_estimand,\n", " econml_estimator=DML(\n", " model_y=GradientBoostingRegressor(),\n", " model_t=GradientBoostingRegressor(),\n", " model_final=LassoCV(fit_intercept=False),\n", " featurizer=PolynomialFeatures(degree=1, include_bias=True),\n", " ),\n", ").fit(\n", " data=data[\"df\"],\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " effect_modifier_names=graph.get_effect_modifiers(treatment_name, outcome_name),\n", ")\n", "\n", "estimate_econml = estimator.estimate_effect(\n", " control_value=0,\n", " treatment_value=1,\n", " target_units=\"ate\",\n", ")\n", "\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# You can call the refute_estimate function for executing several refuters using default parameters\n", "# Currently this function does not support sensitivity_* functions\n", "refutation_results = refute_estimate(\n", " data[\"df\"],\n", " identified_estimand,\n", " estimate,\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " refuters=[refute_bootstrap, refute_data_subset],\n", ")\n", "\n", "for result in refutation_results:\n", " print(result)\n", "\n", "# Or you can execute refute methods directly\n", "# You can change the refute_bootstrap - refute_data_subset for any of the other refuters and add the missing parameters\n", "\n", "bootstrap_refutation = refute_bootstrap(data[\"df\"], identified_estimand, estimate)\n", "print(bootstrap_refutation)\n", "\n", "data_subset_refutation = refute_data_subset(data[\"df\"], identified_estimand, estimate)\n", "print(data_subset_refutation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Backwards Compatibility\n", "\n", "This section shows replicating the same results using only the CausalModel API" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create Causal Model\n", "causal_model = CausalModel(data=data[\"df\"], treatment=treatment_name, outcome=outcome_name, graph=data[\"gml_graph\"])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand_causal_model_api = (\n", " causal_model.identify_effect()\n", ") # graph, treatment and outcome comes from the causal_model object\n", "\n", "print(identified_estimand_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate_causal_model_api = causal_model.estimate_effect(\n", " identified_estimand_causal_model_api, method_name=\"backdoor.propensity_score_matching\"\n", ")\n", "\n", "print(estimate_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bootstrap_refutation_causal_model_api = causal_model.refute_estimate(identified_estimand_causal_model_api, estimate_causal_model_api, \"bootstrap_refuter\")\n", "print(bootstrap_refutation_causal_model_api)\n", "\n", "data_subset_refutation_causal_model_api = causal_model.refute_estimate(\n", " identified_estimand_causal_model_api, estimate_causal_model_api, \"data_subset_refuter\"\n", ")\n", "\n", "print(data_subset_refutation_causal_model_api)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

andresmor-ms

11c4e0dafd6e824eb81ad14262457d954ae61468

affe0952f4aba6845247355c171565510c2c1673

You mean to call `estimate_effect()` without fitting and providing a new data? I'm not sure how that would work, would it be replacing the self._data without the other changes in the `fit()`? Let me know how you expect it to work to be sure I implement it the correct way.

andresmor-ms

py-why/dowhy

Functional api/causal estimators

* Introduce `fit()` method to estimators. * Refactor constructors to avoid using `*args` and `**kwargs` and have more explicit parameters. * Refactor refuters and other parts of the code to use `fit()` and modify arguments to `estimate_effect()`

2022-11-04 16:15:39+00:00

2022-12-03 17:07:53+00:00

docs/source/example_notebooks/dowhy_functional_api.ipynb

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Functional API Preview\n", "\n", "This notebook is part of a set of notebooks that provides a preview of the proposed functional API for dowhy. For details on the new API for DoWhy, check out https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 It is a work-in-progress and is updated as we add new functionality. We welcome your feedback through Discord or on the Discussions page.\n", "This functional API is designed with backwards compatibility. So both the old and new API will continue to co-exist and work for the immediate new releases. Gradually the old API using CausalModel will be deprecated in favor of the new API. \n", "\n", "The current Functional API covers:\n", "* Identify Effect:\n", " * `identify_effect(...)`: Run the identify effect algorithm using defaults just provide the graph, treatment and outcome.\n", " * `auto_identify_effect(...)`: More configurable version of `identify_effect(...)`.\n", " * `id_identify_effect(...)`: Identify Effect using the ID-Algorithm.\n", "* Refute Estimate:\n", " * `refute_estimate`: Function to run a set of the refuters below with the default parameters.\n", " * `refute_bootstrap`: Refute an estimate by running it on a random sample of the data containing measurement error in the confounders.\n", " * `refute_data_subset`: Refute an estimate by rerunning it on a random subset of the original data.\n", " * `refute_random_common_cause`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved).\n", " * `refute_placebo_treatment`: Refute an estimate by replacing treatment with a randomly-generated placebo variable.\n", " * `sensitivity_simulation`: Add an unobserved confounder for refutation (Simulation of an unobserved confounder).\n", " * `sensitivity_linear_partial_r2`: Add an unobserved confounder for refutation (Linear partial R2 : Sensitivity Analysis for linear models).\n", " * `sensitivity_non_parametric_partial_r2`: Add an unobserved confounder for refutation (Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models).\n", " * `sensitivity_e_value`: Computes E-value for point estimate and confidence limits. Benchmarks E-values against measured confounders using Observed Covariate E-values. Plots E-values and Observed\n", " Covariate E-values.\n", " * `refute_dummy_outcome`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import Dependencies" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Functional API imports\n", "from dowhy.causal_identifier import (\n", " BackdoorAdjustment,\n", " EstimandType,\n", " identify_effect,\n", " identify_effect_auto,\n", " identify_effect_id,\n", ") # import effect identifier\n", "from dowhy.causal_refuters import (\n", " refute_bootstrap,\n", " refute_data_subset,\n", " refute_random_common_cause,\n", " refute_placebo_treatment,\n", " sensitivity_e_value,\n", " sensitivity_linear_partial_r2,\n", " sensitivity_non_parametric_partial_r2,\n", " sensitivity_simulation,\n", " refute_dummy_outcome,\n", " refute_estimate,\n", ") # import refuters\n", "\n", "from dowhy.causal_estimators.propensity_score_matching_estimator import PropensityScoreMatchingEstimator\n", "\n", "from dowhy.utils.api import parse_state\n", "\n", "from dowhy.causal_estimator import estimate_effect # Estimate effect function\n", "\n", "from dowhy.causal_graph import CausalGraph\n", "\n", "# Other imports required\n", "from dowhy.datasets import linear_dataset\n", "from dowhy import CausalModel # We still need this as we haven't created the functional API for effect estimation\n", "import econml\n", "\n", "# Config dict to set the logging level\n", "import logging.config\n", "\n", "DEFAULT_LOGGING = {\n", " \"version\": 1,\n", " \"disable_existing_loggers\": False,\n", " \"loggers\": {\n", " \"\": {\n", " \"level\": \"WARN\",\n", " },\n", " },\n", "}\n", "\n", "\n", "# set random seed for deterministic dataset generation \n", "# and avoid problems when running tests\n", "import numpy as np\n", "np.random.seed(1)\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "# Disabling warnings output\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "\n", "warnings.filterwarnings(action=\"ignore\", category=DataConversionWarning)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create the Datasets" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Parameters for creating the Dataset\n", "TREATMENT_IS_BINARY = True\n", "BETA = 10\n", "NUM_SAMPLES = 500\n", "NUM_CONFOUNDERS = 3\n", "NUM_INSTRUMENTS = 2\n", "NUM_EFFECT_MODIFIERS = 2\n", "\n", "# Creating a Linear Dataset with the given parameters\n", "data = linear_dataset(\n", " beta=BETA,\n", " num_common_causes=NUM_CONFOUNDERS,\n", " num_instruments=NUM_INSTRUMENTS,\n", " num_effect_modifiers=NUM_EFFECT_MODIFIERS,\n", " num_samples=NUM_SAMPLES,\n", " treatment_is_binary=True,\n", ")\n", "\n", "treatment_name = data[\"treatment_name\"]\n", "print(treatment_name)\n", "outcome_name = data[\"outcome_name\"]\n", "print(outcome_name)\n", "\n", "graph = CausalGraph(\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " graph=data[\"gml_graph\"],\n", " effect_modifier_names=data[\"effect_modifier_names\"],\n", " common_cause_names=data[\"common_causes_names\"],\n", " observed_node_names=data[\"df\"].columns.tolist(),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Default identify_effect call example:\n", "identified_estimand = identify_effect(graph, treatment_name, outcome_name)\n", "\n", "# auto_identify_effect example with extra parameters:\n", "identified_estimand_auto = identify_effect_auto(\n", " graph,\n", " treatment_name,\n", " outcome_name,\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_EFFICIENT,\n", ")\n", "\n", "# id_identify_effect example:\n", "identified_estimand_id = identify_effect_id(\n", " graph, treatment_name, outcome_name\n", ") # Note that the return type for id_identify_effect is IDExpression and not IdentifiedEstimand\n", "\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Basic Estimate Effect function\n", "\n", "\n", "propensity_score_estimator = PropensityScoreMatchingEstimator(\n", " data=data[\"df\"],\n", " identified_estimand=identified_estimand,\n", " treatment=treatment_name,\n", " outcome=outcome_name,\n", " control_value=0,\n", " treatment_value=1,\n", " test_significance=None,\n", " evaluate_effect_strength=False,\n", " confidence_intervals=False,\n", " target_units=\"ate\",\n", " effect_modifiers=graph.get_effect_modifiers(treatment_name, outcome_name),\n", ")\n", "\n", "estimate = estimate_effect(\n", " treatment=treatment_name,\n", " outcome=outcome_name,\n", " identified_estimand=identified_estimand,\n", " identifier_name=\"backdoor\",\n", " method=propensity_score_estimator,\n", ")\n", "\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# You can call the refute_estimate function for executing several refuters using default parameters\n", "# Currently this function does not support sensitivity_* functions\n", "refutation_results = refute_estimate(\n", " data[\"df\"],\n", " identified_estimand,\n", " estimate,\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " refuters=[refute_bootstrap, refute_data_subset],\n", ")\n", "\n", "for result in refutation_results:\n", " print(result)\n", "\n", "# Or you can execute refute methods directly\n", "# You can change the refute_bootstrap - refute_data_subset for any of the other refuters and add the missing parameters\n", "\n", "bootstrap_refutation = refute_bootstrap(data[\"df\"], identified_estimand, estimate)\n", "print(bootstrap_refutation)\n", "\n", "data_subset_refutation = refute_data_subset(data[\"df\"], identified_estimand, estimate)\n", "print(data_subset_refutation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Backwards Compatibility\n", "\n", "This section shows replicating the same results using only the CausalModel API" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create Causal Model\n", "causal_model = CausalModel(data=data[\"df\"], treatment=treatment_name, outcome=outcome_name, graph=data[\"gml_graph\"])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand_causal_model_api = (\n", " causal_model.identify_effect()\n", ") # graph, treatment and outcome comes from the causal_model object\n", "\n", "print(identified_estimand_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate_causal_model_api = causal_model.estimate_effect(\n", " identified_estimand_causal_model_api, method_name=\"backdoor.propensity_score_matching\"\n", ")\n", "\n", "print(estimate_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bootstrap_refutation_causal_model_api = causal_model.refute_estimate(identified_estimand_causal_model_api, estimate_causal_model_api, \"bootstrap_refuter\")\n", "print(bootstrap_refutation_causal_model_api)\n", "\n", "data_subset_refutation_causal_model_api = causal_model.refute_estimate(\n", " identified_estimand_causal_model_api, estimate_causal_model_api, \"data_subset_refuter\"\n", ")\n", "\n", "print(data_subset_refutation_causal_model_api)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Functional API Preview\n", "\n", "This notebook is part of a set of notebooks that provides a preview of the proposed functional API for dowhy. For details on the new API for DoWhy, check out https://github.com/py-why/dowhy/wiki/API-proposal-for-v1 It is a work-in-progress and is updated as we add new functionality. We welcome your feedback through Discord or on the Discussions page.\n", "This functional API is designed with backwards compatibility. So both the old and new API will continue to co-exist and work for the immediate new releases. Gradually the old API using CausalModel will be deprecated in favor of the new API. \n", "\n", "The current Functional API covers:\n", "* Identify Effect:\n", " * `identify_effect(...)`: Run the identify effect algorithm using defaults just provide the graph, treatment and outcome.\n", " * `auto_identify_effect(...)`: More configurable version of `identify_effect(...)`.\n", " * `id_identify_effect(...)`: Identify Effect using the ID-Algorithm.\n", "* Refute Estimate:\n", " * `refute_estimate`: Function to run a set of the refuters below with the default parameters.\n", " * `refute_bootstrap`: Refute an estimate by running it on a random sample of the data containing measurement error in the confounders.\n", " * `refute_data_subset`: Refute an estimate by rerunning it on a random subset of the original data.\n", " * `refute_random_common_cause`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved).\n", " * `refute_placebo_treatment`: Refute an estimate by replacing treatment with a randomly-generated placebo variable.\n", " * `sensitivity_simulation`: Add an unobserved confounder for refutation (Simulation of an unobserved confounder).\n", " * `sensitivity_linear_partial_r2`: Add an unobserved confounder for refutation (Linear partial R2 : Sensitivity Analysis for linear models).\n", " * `sensitivity_non_parametric_partial_r2`: Add an unobserved confounder for refutation (Non-Parametric partial R2 based : Sensitivity Analyis for non-parametric models).\n", " * `sensitivity_e_value`: Computes E-value for point estimate and confidence limits. Benchmarks E-values against measured confounders using Observed Covariate E-values. Plots E-values and Observed\n", " Covariate E-values.\n", " * `refute_dummy_outcome`: Refute an estimate by introducing a randomly generated confounder (that may have been unobserved)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import Dependencies" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Functional API imports\n", "from dowhy.causal_identifier import (\n", " BackdoorAdjustment,\n", " EstimandType,\n", " identify_effect,\n", " identify_effect_auto,\n", " identify_effect_id,\n", ") # import effect identifier\n", "from dowhy.causal_refuters import (\n", " refute_bootstrap,\n", " refute_data_subset,\n", " refute_random_common_cause,\n", " refute_placebo_treatment,\n", " sensitivity_e_value,\n", " sensitivity_linear_partial_r2,\n", " sensitivity_non_parametric_partial_r2,\n", " sensitivity_simulation,\n", " refute_dummy_outcome,\n", " refute_estimate,\n", ") # import refuters\n", "\n", "from dowhy.causal_estimators.propensity_score_matching_estimator import PropensityScoreMatchingEstimator\n", "from dowhy.causal_estimators.econml import Econml\n", "\n", "from dowhy.utils.api import parse_state\n", "\n", "from dowhy.causal_estimator import estimate_effect # Estimate effect function\n", "\n", "from dowhy.causal_graph import CausalGraph\n", "\n", "# Other imports required\n", "from dowhy.datasets import linear_dataset\n", "from dowhy import CausalModel # We still need this as we haven't created the functional API for effect estimation\n", "import econml\n", "\n", "# Config dict to set the logging level\n", "import logging.config\n", "\n", "DEFAULT_LOGGING = {\n", " \"version\": 1,\n", " \"disable_existing_loggers\": False,\n", " \"loggers\": {\n", " \"\": {\n", " \"level\": \"WARN\",\n", " },\n", " },\n", "}\n", "\n", "\n", "# set random seed for deterministic dataset generation \n", "# and avoid problems when running tests\n", "import numpy as np\n", "np.random.seed(1)\n", "\n", "logging.config.dictConfig(DEFAULT_LOGGING)\n", "# Disabling warnings output\n", "import warnings\n", "from sklearn.exceptions import DataConversionWarning\n", "\n", "warnings.filterwarnings(action=\"ignore\", category=DataConversionWarning)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create the Datasets" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Parameters for creating the Dataset\n", "TREATMENT_IS_BINARY = True\n", "BETA = 10\n", "NUM_SAMPLES = 500\n", "NUM_CONFOUNDERS = 3\n", "NUM_INSTRUMENTS = 2\n", "NUM_EFFECT_MODIFIERS = 2\n", "\n", "# Creating a Linear Dataset with the given parameters\n", "data = linear_dataset(\n", " beta=BETA,\n", " num_common_causes=NUM_CONFOUNDERS,\n", " num_instruments=NUM_INSTRUMENTS,\n", " num_effect_modifiers=NUM_EFFECT_MODIFIERS,\n", " num_samples=NUM_SAMPLES,\n", " treatment_is_binary=True,\n", ")\n", "\n", "data_2 = linear_dataset(\n", " beta=BETA,\n", " num_common_causes=NUM_CONFOUNDERS,\n", " num_instruments=NUM_INSTRUMENTS,\n", " num_effect_modifiers=NUM_EFFECT_MODIFIERS,\n", " num_samples=NUM_SAMPLES,\n", " treatment_is_binary=True,\n", ")\n", "\n", "treatment_name = data[\"treatment_name\"]\n", "print(treatment_name)\n", "outcome_name = data[\"outcome_name\"]\n", "print(outcome_name)\n", "\n", "graph = CausalGraph(\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " graph=data[\"gml_graph\"],\n", " effect_modifier_names=data[\"effect_modifier_names\"],\n", " common_cause_names=data[\"common_causes_names\"],\n", " observed_node_names=data[\"df\"].columns.tolist(),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Default identify_effect call example:\n", "identified_estimand = identify_effect(graph, treatment_name, outcome_name)\n", "\n", "# auto_identify_effect example with extra parameters:\n", "identified_estimand_auto = identify_effect_auto(\n", " graph,\n", " treatment_name,\n", " outcome_name,\n", " estimand_type=EstimandType.NONPARAMETRIC_ATE,\n", " backdoor_adjustment=BackdoorAdjustment.BACKDOOR_EFFICIENT,\n", ")\n", "\n", "# id_identify_effect example:\n", "identified_estimand_id = identify_effect_id(\n", " graph, treatment_name, outcome_name\n", ") # Note that the return type for id_identify_effect is IDExpression and not IdentifiedEstimand\n", "\n", "print(identified_estimand)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Basic Estimate Effect function\n", "estimator = PropensityScoreMatchingEstimator(\n", " identified_estimand=identified_estimand,\n", " test_significance=None,\n", " evaluate_effect_strength=False,\n", " confidence_intervals=False,\n", ").fit(\n", " data=data[\"df\"],\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " effect_modifier_names=graph.get_effect_modifiers(treatment_name, outcome_name),\n", ")\n", "\n", "estimate = estimator.estimate_effect(\n", " control_value=0,\n", " treatment_value=1,\n", " target_units=\"ate\",\n", ")\n", "\n", "# Using same estimator with different data\n", "second_estimate = estimator.estimate_effect(\n", " data=data_2[\"df\"],\n", " control_value=0,\n", " treatment_value=1,\n", " target_units=\"ate\",\n", ")\n", "\n", "print(estimate)\n", "print(\"-----------\")\n", "print(second_estimate)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# EconML estimator example\n", "from econml.dml import DML\n", "from sklearn.linear_model import LassoCV\n", "from sklearn.preprocessing import PolynomialFeatures\n", "\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "\n", "estimator = Econml(\n", " identified_estimand=identified_estimand,\n", " econml_estimator=DML(\n", " model_y=GradientBoostingRegressor(),\n", " model_t=GradientBoostingRegressor(),\n", " model_final=LassoCV(fit_intercept=False),\n", " featurizer=PolynomialFeatures(degree=1, include_bias=True),\n", " ),\n", ").fit(\n", " data=data[\"df\"],\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " effect_modifier_names=graph.get_effect_modifiers(treatment_name, outcome_name),\n", ")\n", "\n", "estimate_econml = estimator.estimate_effect(\n", " control_value=0,\n", " treatment_value=1,\n", " target_units=\"ate\",\n", ")\n", "\n", "print(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate - Functional API (Preview)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# You can call the refute_estimate function for executing several refuters using default parameters\n", "# Currently this function does not support sensitivity_* functions\n", "refutation_results = refute_estimate(\n", " data[\"df\"],\n", " identified_estimand,\n", " estimate,\n", " treatment_name=treatment_name,\n", " outcome_name=outcome_name,\n", " refuters=[refute_bootstrap, refute_data_subset],\n", ")\n", "\n", "for result in refutation_results:\n", " print(result)\n", "\n", "# Or you can execute refute methods directly\n", "# You can change the refute_bootstrap - refute_data_subset for any of the other refuters and add the missing parameters\n", "\n", "bootstrap_refutation = refute_bootstrap(data[\"df\"], identified_estimand, estimate)\n", "print(bootstrap_refutation)\n", "\n", "data_subset_refutation = refute_data_subset(data[\"df\"], identified_estimand, estimate)\n", "print(data_subset_refutation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Backwards Compatibility\n", "\n", "This section shows replicating the same results using only the CausalModel API" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create Causal Model\n", "causal_model = CausalModel(data=data[\"df\"], treatment=treatment_name, outcome=outcome_name, graph=data[\"gml_graph\"])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identify Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "identified_estimand_causal_model_api = (\n", " causal_model.identify_effect()\n", ") # graph, treatment and outcome comes from the causal_model object\n", "\n", "print(identified_estimand_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate Effect" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "estimate_causal_model_api = causal_model.estimate_effect(\n", " identified_estimand_causal_model_api, method_name=\"backdoor.propensity_score_matching\"\n", ")\n", "\n", "print(estimate_causal_model_api)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Refute Estimate" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bootstrap_refutation_causal_model_api = causal_model.refute_estimate(identified_estimand_causal_model_api, estimate_causal_model_api, \"bootstrap_refuter\")\n", "print(bootstrap_refutation_causal_model_api)\n", "\n", "data_subset_refutation_causal_model_api = causal_model.refute_estimate(\n", " identified_estimand_causal_model_api, estimate_causal_model_api, \"data_subset_refuter\"\n", ")\n", "\n", "print(data_subset_refutation_causal_model_api)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 4 }

andresmor-ms

11c4e0dafd6e824eb81ad14262457d954ae61468

affe0952f4aba6845247355c171565510c2c1673

no, I meant that you fit an estimator once, and then call estimate_effect twice for two different datasets. Just to show that we can fit once, and then call estimate_effect multiple times.

amit-sharma

py-why/dowhy

Functional api/causal estimators

* Introduce `fit()` method to estimators. * Refactor constructors to avoid using `*args` and `**kwargs` and have more explicit parameters. * Refactor refuters and other parts of the code to use `fit()` and modify arguments to `estimate_effect()`

2022-11-04 16:15:39+00:00

2022-12-03 17:07:53+00:00

docs/source/example_notebooks/sensitivity_analysis_nonparametric_estimators.ipynb

{ "cells": [ { "cell_type": "markdown", "id": "0bbaacaa", "metadata": {}, "source": [ "# Sensitivity analysis for non-parametric causal estimators\n", "Sensitivity analysis helps us study how robust an estimated effect is when the assumption of no unobserved confounding is violated. That is, how much bias does our estimate have due to omitting an (unobserved) confounder? Known as the \n", "*omitted variable bias (OVB)*, it gives us a measure of how the inclusion of an omitted common cause (confounder) would have changed the estimated effect. \n", "\n", "This notebook shows how to estimate the OVB for general, non-parametric causal estimators. For gaining intuition, we suggest going through an introductory notebook that describes how to estimate OVB for a a linear estimator: [Sensitivity analysis for linear estimators](https://github.com/py-why/dowhy/blob/master/docs/source/example_notebooks/sensitivity_analysis_testing.ipynb). To recap, in that notebook, we saw how the OVB depended on linear partial R^2 values and used this insight to compute the adjusted estimate values depending on the relative strength of the confounder with the outcome and treatment. We now generalize the technique using the non-parametric partial R^2 and Reisz representers.\n", "\n", "\n", "This notebook is based on *Chernozhukov et al., Long Story Short: Omitted Variable Bias in Causal Machine Learning. https://arxiv.org/abs/2112.13398*. " ] }, { "cell_type": "markdown", "id": "cf30b925", "metadata": {}, "source": [ "## I. Sensitivity analysis for partially linear models\n", "We first analyze the sensitivity of a causal estimate when the true data-generating process (DGP) is known to be partially linear. That is, the outcome can be additively decomposed into a linear function of the treatment and a non-linear function of the confounders. We denote the treatment by $T$, outcome by $Y$, observed confounders by $W$ and unobserved confounders by $U$. \n", "$$ Y = g(T, W, U) + \\epsilon = \\theta T + h(W, U) + \\epsilon $$\n", "\n", "However, we cannot estimate the above equation because the confounders $U$ are unobserved. Thus, in practice, a causal estimator uses the following \"short\" equation, \n", "$$ Y = g_s(T, W) + \\epsilon_s = \\theta_s T + h_s(W) + \\epsilon_s $$\n", "\n", "The goal of sensitivity analysis is to answer how far $\\theta_s$ would be from the true $\\theta$. Chernozhukov et al. show that given a special function called Reisz function $\\alpha$, the omitted variable bias, $|\\theta - \\theta_s|$ is bounded by $\\sqrt{E[g-g_s]^2E[\\alpha-\\alpha_s]^2}$. For partial linear models, $\\alpha$ and the \"short\" $\\alpha_s$ are defined as, \n", "$$ \\alpha := \\frac{T - E[T | W, U] )}{E(T - E[T | W, U]) ^ 2}$$\n", "$$ \\alpha_s := \\frac{(T - E[T | W] )}{E(T - E[T | W]) ^ 2} $$\n", "\n", "The bound can be expressed in terms of the *partial* R^2 of the unobserved confounder $U$ with the treatment and outcome, conditioned on the observed confounders $W$. Recall that R^2 of $U$ wrt some target $Z$ is defined as the ratio of variance of the prediction $E[Z|U]$ with the variance of $Z$, $R^2_{Z\\sim U}=\\frac{\\operatorname{Var}(E[Z|U])}{\\operatorname{Var}(Y)}$. We can define the partial R^2 as an extension that measures the additional gain in explanatory power conditioned on some variables $W$. \n", "$$ \\eta^2_{Z\\sim U| W} = \\frac{\\operatorname{Var}(E[Z|W, U]) - \\operatorname{Var}(E[Z|W])}{\\operatorname{Var}(Z) - \\operatorname{Var}(E[Z|W])} $$\n", "\n", "The bound is given by, \n", "$$ (\\theta - \\theta_s)^2 = E[g-g_s]^2E[\\alpha-\\alpha_s]^2 = S^2 C_Y^2 C_T^2 $$ \n", "where, \n", "$$ S^2 = \\frac{E[(Y-g_s)^2]}{E[\\alpha_s^2]}; \\ \\ C_Y^2 = \\eta^2_{Y \\sim U | T, W}, \\ \\ C_T^2 = \\frac{\\eta^2_{T\\sim U | W}}{1 - \\eta^2_{T\\sim U | W}}$$\n", "\n", "\n", "$S^2$ can be estimated from data. The other two parameters need to be specified manually: they convey the strength of the unobserved confounder $U$ on treatment and outcome. Below we show how to create a sensitivity contour plot by specifying a range of plausible values for $\\eta^2_{Y \\sim U | T, W}$ and $\\eta^2_{T\\sim U | W}$. We also show how to benchmark and set these values as a fraction of the maximum partial R^2 due to any subset of the observed covariates. " ] }, { "cell_type": "markdown", "id": "1b67b63e", "metadata": {}, "source": [ "### Creating a dataset with unobserved confounding " ] }, { "cell_type": "code", "execution_count": null, "id": "bbbab4ea", "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "id": "ba6f68b9", "metadata": {}, "outputs": [], "source": [ "# Required libraries\n", "import re\n", "import numpy as np\n", "import dowhy\n", "from dowhy import CausalModel\n", "import dowhy.datasets\n", "from dowhy.utils.regression import create_polynomial_function" ] }, { "cell_type": "markdown", "id": "2c386282", "metadata": {}, "source": [ "We create a dataset with linear relationship between treatment and outcome, following the partial linear data-generating process. $\\beta$ is the true causal effect." ] }, { "cell_type": "code", "execution_count": null, "id": "41c60ca7", "metadata": {}, "outputs": [], "source": [ "np.random.seed(101) \n", "data = dowhy.datasets.partially_linear_dataset(beta = 10,\n", " num_common_causes = 7,\n", " num_unobserved_common_causes=1,\n", " strength_unobserved_confounding=10,\n", " num_samples = 1000,\n", " num_treatments = 1,\n", " stddev_treatment_noise = 10,\n", " stddev_outcome_noise = 5\n", " )\n", "display(data)" ] }, { "cell_type": "markdown", "id": "5df879f9", "metadata": {}, "source": [ "The true ATE for this data-generating process is," ] }, { "cell_type": "code", "execution_count": null, "id": "75882711", "metadata": {}, "outputs": [], "source": [ "data[\"ate\"]" ] }, { "cell_type": "markdown", "id": "5308f4dc", "metadata": {}, "source": [ "To simulate unobserved confounding, we remove one of the common causes from the dataset. \n" ] }, { "cell_type": "code", "execution_count": null, "id": "636b6a25", "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Observed data \n", "dropped_cols=[\"W0\"]\n", "user_data = data[\"df\"].drop(dropped_cols, axis = 1)\n", "# assumed graph\n", "user_graph = data[\"gml_graph\"]\n", "for col in dropped_cols:\n", " user_graph = user_graph.replace('node[ id \"{0}\" label \"{0}\"]'.format(col), '')\n", " user_graph = re.sub('edge\\[ source \"{}\" target \"[vy][0]*\"\\]'.format(col), \"\", user_graph)\n", "user_data" ] }, { "cell_type": "markdown", "id": "4ae95e95", "metadata": {}, "source": [ "### Obtaining a causal estimate using Model, Identify, Estimate steps\n", "Create a causal model with the \"observed\" data and causal graph." ] }, { "cell_type": "code", "execution_count": null, "id": "207034e5", "metadata": {}, "outputs": [], "source": [ "model = CausalModel(\n", " data=user_data,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=user_graph,\n", " test_significance=None,\n", " )\n", "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "code", "execution_count": null, "id": "4eaec5dc", "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Identify effect\n", "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "code", "execution_count": null, "id": "56889b39", "metadata": {}, "outputs": [], "source": [ "# Estimate effect\n", "import econml\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "linear_dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.LinearDML\",\n", " method_params={\n", " 'init_params': {'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " 'linear_first_stages': False\n", " },\n", " 'fit_params': {'cache_values': True,}\n", " })\n", "print(linear_dml_estimate)" ] }, { "cell_type": "markdown", "id": "891068cb", "metadata": {}, "source": [ "### Sensitivity Analysis using the Refute step\n", "After estimation , we need to check how robust our estimate is against the possibility of unobserved confounders. We perform sensitivity analysis for the LinearDML estimator assuming that its assumption on data-generating process holds: the true function for $Y$ is partial linear. For computational efficiency, we set <b>cache_values</b> = <b>True</b> in `fit_params` to cache the results of first stage estimation.\n", "\n", "Parameters used:\n", "\n", "* <b>method_name</b>: Refutation method name <br>\n", "* <b>simulation_method</b>: \"non-parametric-partial-R2\" for non Parametric Sensitivity Analysis. \n", "Note that partial linear sensitivity analysis is automatically chosen if LinearDML estimator is used for estimation. \n", "* **partial_r2_confounder_treatment**: $\\eta^2_{T\\sim U | W}$, Partial R2 of unobserved confounder with treatment conditioned on all observed confounders. \n", "* **partial_r2_confounder_outcome**: $\\eta^2_{Y \\sim U | T, W}$, Partial R2 of unobserved confounder with outcome conditioned on treatment and all observed confounders. " ] }, { "cell_type": "code", "execution_count": null, "id": "2488ccbb", "metadata": {}, "outputs": [], "source": [ "refute = model.refute_estimate(identified_estimand, linear_dml_estimate ,\n", " method_name = \"add_unobserved_common_cause\",\n", " simulation_method = \"non-parametric-partial-R2\",\n", " partial_r2_confounder_treatment = np.arange(0, 0.8, 0.1),\n", " partial_r2_confounder_outcome = np.arange(0, 0.8, 0.1)\n", " )\n", "print(refute)" ] }, { "cell_type": "markdown", "id": "81f1d65b", "metadata": {}, "source": [ "**Intepretation of the plot.** In the above plot, the x-axis shows hypothetical partial R2 values of unobserved confounder(s) with the treatment. The y-axis shows hypothetical partial R2 of unobserved confounder(s) with the outcome. At <x=0,y=0>, the black diamond shows the original estimate (theta_s) without considering the unobserved confounders.\n", "\n", "The contour levels represent *adjusted* lower confidence bound estimate of the effect, which would be obtained if the unobserved confounder(s) had been included in the estimation model. The red contour line is the critical threshold where the adjusted effect goes to zero. Thus, confounders with such strength or stronger are sufficient to reverse the sign of the estimated effect and invalidate the estimate's conclusions. This notion can be quantified by outputting the robustness value." ] }, { "cell_type": "code", "execution_count": null, "id": "52b2e904", "metadata": {}, "outputs": [], "source": [ "refute.RV" ] }, { "cell_type": "markdown", "id": "3524cb07", "metadata": {}, "source": [ "The robustness value measures the minimal equal strength of $\\eta^2_{T\\sim U | W}$ and $\\eta^2_{Y \\sim U | T, W}$ such the bound for the average treatment effect would include zero. It can be between 0 and 1. <br>\n", "A robustness value of 0.45 implies that confounders with $\\eta^2_{T\\sim U | W}$ and $\\eta^2_{Y \\sim U | T, W}$ values less than 0.4 would not be sufficient enough to bring down the estimates to zero. In general, a low robustness value implies that the results can be changed even by the presence of weak confounders whereas a robustness value close to 1 means the treatment effect can handle even strong confounders that may explain all residual variation of the treatment and the outcome." ] }, { "cell_type": "markdown", "id": "a1fbcf48", "metadata": {}, "source": [ "**Benchmarking.** In general, however, providing a plausible range of partial R2 values is difficult. Instead, we can infer the partial R2 of the unobserved confounder as a multiple of the partial R2 of any subset of observed confounders. So now we just need to specify the effect of unobserved confounding as a multiple/fraction of the observed confounding. This process is known as *benchmarking*." ] }, { "cell_type": "markdown", "id": "7a1f4986", "metadata": {}, "source": [ "The relevant arguments for bencmarking are:\n", "- <b>benchmark_common_causes</b>: Names of the observed confounders used to bound the strengths of unobserved confounder<br>\n", "- <b>effect_fraction_on_treatment</b>: Strength of association between unobserved confounder and treatment compared to benchmark confounders<br>\n", "- <b>effect_fraction_on_outcome</b>: Strength of association between unobserved confounder and outcome compared to benchmark confounders<br>" ] }, { "cell_type": "code", "execution_count": null, "id": "85eefe08", "metadata": {}, "outputs": [], "source": [ "refute_bm = model.refute_estimate(identified_estimand, linear_dml_estimate ,\n", " method_name = \"add_unobserved_common_cause\",\n", " simulation_method = \"non-parametric-partial-R2\",\n", " benchmark_common_causes = [\"W1\"],\n", " effect_fraction_on_treatment = 0.2,\n", " effect_fraction_on_outcome = 0.2\n", " )" ] }, { "cell_type": "markdown", "id": "46b54056", "metadata": {}, "source": [ "The red triangle shows the estimated partial-R^2 of a chosen benchmark observed covariate with the treatment and outcome. In the above call, we chose *W1* as the benchmark covariate. Under assumption that the unobserved confounder cannot be stronger in its effect on treatment and outcome than the observed benchmark covariate (*W1*), the above plot shows that the mean estimated effect will reduce after accounting for unobserved confounding, but still remain substantially above zero.\n" ] }, { "cell_type": "markdown", "id": "070f01c6", "metadata": {}, "source": [ "**Plot types**. The default `plot_type` is to show the `lower_confidence_bound` under a significance level . Other possible values for the `plot_type` are:\n", "* `upper_confidence_bound`: preferably used in cases where the unobserved confounder is expected to lower the estimate.\n", "* `lower_ate_bound`: lower (point) estimate for unconfounded average treatment effect without considering the significance level\n", "* `upper_ate_bound`: upper (point) estimate for unconfounded average treatment effect without considering the significance level\n", "* `bias`: the bias of the obtained estimate compared to the true estimate" ] }, { "cell_type": "code", "execution_count": null, "id": "df23a49b", "metadata": {}, "outputs": [], "source": [ "refute_bm.plot(plot_type = \"upper_confidence_bound\")\n", "refute_bm.plot(plot_type = \"bias\")" ] }, { "cell_type": "markdown", "id": "83052508", "metadata": {}, "source": [ "We can also access the benchmarking results as a data frame." ] }, { "cell_type": "code", "execution_count": null, "id": "934eef00", "metadata": {}, "outputs": [], "source": [ "refute_bm.results" ] }, { "cell_type": "markdown", "id": "1fffe64f", "metadata": {}, "source": [ "## II. Sensitivity Analysis for general non-parametric models\n", "We now perform sensitivity analysis without making any assumption on the true data-generating process. The sensitivity still depends on the partial R2 of unobserved confounder with outcome, $\\eta^2_{Y \\sim U | T, W}$, and a similar parameter for the confounder-treatment relationship. However, the computation of bounds is more complicated and requires estimation of a special function known as reisz function. Refer to Chernozhukov et al. for details." ] }, { "cell_type": "code", "execution_count": null, "id": "7cff3837", "metadata": {}, "outputs": [], "source": [ "# Estimate effect using a non-parametric estimator\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "estimate_npar = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.KernelDML\",\n", " method_params={\n", " 'init_params': {'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(), },\n", " 'fit_params': {},\n", " })\n", "print(estimate_npar)" ] }, { "cell_type": "markdown", "id": "5c971de4", "metadata": {}, "source": [ "To do the sensitivity analysis, we now use the same `non-parametric--partial-R2` method, however the estimation of partial R2 will be based on reisz representers. We use `plugin_reisz=True` to specify that we will be using a plugin reisz function estimator (this is faster and available for binary treatments). Otherwise, we can set it to `False` to estimate reisz function using a loss function." ] }, { "cell_type": "code", "execution_count": null, "id": "946e1237", "metadata": { "scrolled": true }, "outputs": [], "source": [ "refute_npar = model.refute_estimate(identified_estimand, estimate_npar,\n", " method_name = \"add_unobserved_common_cause\",\n", " simulation_method = \"non-parametric-partial-R2\",\n", " benchmark_common_causes = [\"W1\"],\n", " effect_fraction_on_treatment = 0.2,\n", " effect_fraction_on_outcome = 0.2,\n", " plugin_reisz=True\n", " )\n", "print(refute_npar)" ] }, { "cell_type": "markdown", "id": "db63007e", "metadata": {}, "source": [ "The plot has the same interpretation as before. We obtain a robustness value of 0.66 compared to robustness value of 0.45 for LinearDML estimator.\n", "\n", "Note that the robustness value changes, even though the point estimates from LinearDML and KernelDML are similar. This is because we made different assumptions on the true data-generating process. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }

{ "cells": [ { "cell_type": "markdown", "id": "0bbaacaa", "metadata": {}, "source": [ "# Sensitivity analysis for non-parametric causal estimators\n", "Sensitivity analysis helps us study how robust an estimated effect is when the assumption of no unobserved confounding is violated. That is, how much bias does our estimate have due to omitting an (unobserved) confounder? Known as the \n", "*omitted variable bias (OVB)*, it gives us a measure of how the inclusion of an omitted common cause (confounder) would have changed the estimated effect. \n", "\n", "This notebook shows how to estimate the OVB for general, non-parametric causal estimators. For gaining intuition, we suggest going through an introductory notebook that describes how to estimate OVB for a a linear estimator: [Sensitivity analysis for linear estimators](https://github.com/py-why/dowhy/blob/master/docs/source/example_notebooks/sensitivity_analysis_testing.ipynb). To recap, in that notebook, we saw how the OVB depended on linear partial R^2 values and used this insight to compute the adjusted estimate values depending on the relative strength of the confounder with the outcome and treatment. We now generalize the technique using the non-parametric partial R^2 and Reisz representers.\n", "\n", "\n", "This notebook is based on *Chernozhukov et al., Long Story Short: Omitted Variable Bias in Causal Machine Learning. https://arxiv.org/abs/2112.13398*. " ] }, { "cell_type": "markdown", "id": "cf30b925", "metadata": {}, "source": [ "## I. Sensitivity analysis for partially linear models\n", "We first analyze the sensitivity of a causal estimate when the true data-generating process (DGP) is known to be partially linear. That is, the outcome can be additively decomposed into a linear function of the treatment and a non-linear function of the confounders. We denote the treatment by $T$, outcome by $Y$, observed confounders by $W$ and unobserved confounders by $U$. \n", "$$ Y = g(T, W, U) + \\epsilon = \\theta T + h(W, U) + \\epsilon $$\n", "\n", "However, we cannot estimate the above equation because the confounders $U$ are unobserved. Thus, in practice, a causal estimator uses the following \"short\" equation, \n", "$$ Y = g_s(T, W) + \\epsilon_s = \\theta_s T + h_s(W) + \\epsilon_s $$\n", "\n", "The goal of sensitivity analysis is to answer how far $\\theta_s$ would be from the true $\\theta$. Chernozhukov et al. show that given a special function called Reisz function $\\alpha$, the omitted variable bias, $|\\theta - \\theta_s|$ is bounded by $\\sqrt{E[g-g_s]^2E[\\alpha-\\alpha_s]^2}$. For partial linear models, $\\alpha$ and the \"short\" $\\alpha_s$ are defined as, \n", "$$ \\alpha := \\frac{T - E[T | W, U] )}{E(T - E[T | W, U]) ^ 2}$$\n", "$$ \\alpha_s := \\frac{(T - E[T | W] )}{E(T - E[T | W]) ^ 2} $$\n", "\n", "The bound can be expressed in terms of the *partial* R^2 of the unobserved confounder $U$ with the treatment and outcome, conditioned on the observed confounders $W$. Recall that R^2 of $U$ wrt some target $Z$ is defined as the ratio of variance of the prediction $E[Z|U]$ with the variance of $Z$, $R^2_{Z\\sim U}=\\frac{\\operatorname{Var}(E[Z|U])}{\\operatorname{Var}(Y)}$. We can define the partial R^2 as an extension that measures the additional gain in explanatory power conditioned on some variables $W$. \n", "$$ \\eta^2_{Z\\sim U| W} = \\frac{\\operatorname{Var}(E[Z|W, U]) - \\operatorname{Var}(E[Z|W])}{\\operatorname{Var}(Z) - \\operatorname{Var}(E[Z|W])} $$\n", "\n", "The bound is given by, \n", "$$ (\\theta - \\theta_s)^2 = E[g-g_s]^2E[\\alpha-\\alpha_s]^2 = S^2 C_Y^2 C_T^2 $$ \n", "where, \n", "$$ S^2 = \\frac{E[(Y-g_s)^2]}{E[\\alpha_s^2]}; \\ \\ C_Y^2 = \\eta^2_{Y \\sim U | T, W}, \\ \\ C_T^2 = \\frac{\\eta^2_{T\\sim U | W}}{1 - \\eta^2_{T\\sim U | W}}$$\n", "\n", "\n", "$S^2$ can be estimated from data. The other two parameters need to be specified manually: they convey the strength of the unobserved confounder $U$ on treatment and outcome. Below we show how to create a sensitivity contour plot by specifying a range of plausible values for $\\eta^2_{Y \\sim U | T, W}$ and $\\eta^2_{T\\sim U | W}$. We also show how to benchmark and set these values as a fraction of the maximum partial R^2 due to any subset of the observed covariates. " ] }, { "cell_type": "markdown", "id": "1b67b63e", "metadata": {}, "source": [ "### Creating a dataset with unobserved confounding " ] }, { "cell_type": "code", "execution_count": null, "id": "bbbab4ea", "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": null, "id": "ba6f68b9", "metadata": {}, "outputs": [], "source": [ "# Required libraries\n", "import re\n", "import numpy as np\n", "import dowhy\n", "from dowhy import CausalModel\n", "import dowhy.datasets\n", "from dowhy.utils.regression import create_polynomial_function" ] }, { "cell_type": "markdown", "id": "2c386282", "metadata": {}, "source": [ "We create a dataset with linear relationship between treatment and outcome, following the partial linear data-generating process. $\\beta$ is the true causal effect." ] }, { "cell_type": "code", "execution_count": null, "id": "41c60ca7", "metadata": {}, "outputs": [], "source": [ "np.random.seed(101) \n", "data = dowhy.datasets.partially_linear_dataset(beta = 10,\n", " num_common_causes = 7,\n", " num_unobserved_common_causes=1,\n", " strength_unobserved_confounding=10,\n", " num_samples = 1000,\n", " num_treatments = 1,\n", " stddev_treatment_noise = 10,\n", " stddev_outcome_noise = 5\n", " )\n", "display(data)" ] }, { "cell_type": "markdown", "id": "5df879f9", "metadata": {}, "source": [ "The true ATE for this data-generating process is," ] }, { "cell_type": "code", "execution_count": null, "id": "75882711", "metadata": {}, "outputs": [], "source": [ "data[\"ate\"]" ] }, { "cell_type": "markdown", "id": "5308f4dc", "metadata": {}, "source": [ "To simulate unobserved confounding, we remove one of the common causes from the dataset. \n" ] }, { "cell_type": "code", "execution_count": null, "id": "636b6a25", "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Observed data \n", "dropped_cols=[\"W0\"]\n", "user_data = data[\"df\"].drop(dropped_cols, axis = 1)\n", "# assumed graph\n", "user_graph = data[\"gml_graph\"]\n", "for col in dropped_cols:\n", " user_graph = user_graph.replace('node[ id \"{0}\" label \"{0}\"]'.format(col), '')\n", " user_graph = re.sub('edge\\[ source \"{}\" target \"[vy][0]*\"\\]'.format(col), \"\", user_graph)\n", "user_data" ] }, { "cell_type": "markdown", "id": "4ae95e95", "metadata": {}, "source": [ "### Obtaining a causal estimate using Model, Identify, Estimate steps\n", "Create a causal model with the \"observed\" data and causal graph." ] }, { "cell_type": "code", "execution_count": null, "id": "207034e5", "metadata": {}, "outputs": [], "source": [ "model = CausalModel(\n", " data=user_data,\n", " treatment=data[\"treatment_name\"],\n", " outcome=data[\"outcome_name\"],\n", " graph=user_graph,\n", " test_significance=None,\n", " )\n", "model.view_model()\n", "from IPython.display import Image, display\n", "display(Image(filename=\"causal_model.png\"))" ] }, { "cell_type": "code", "execution_count": null, "id": "4eaec5dc", "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Identify effect\n", "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n", "print(identified_estimand)" ] }, { "cell_type": "code", "execution_count": null, "id": "56889b39", "metadata": {}, "outputs": [], "source": [ "# Estimate effect\n", "import econml\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "linear_dml_estimate = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.dml.LinearDML\",\n", " method_params={\n", " 'init_params': {'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(),\n", " 'linear_first_stages': False\n", " },\n", " 'fit_params': {'cache_values': True,}\n", " })\n", "print(linear_dml_estimate)" ] }, { "cell_type": "markdown", "id": "891068cb", "metadata": {}, "source": [ "### Sensitivity Analysis using the Refute step\n", "After estimation , we need to check how robust our estimate is against the possibility of unobserved confounders. We perform sensitivity analysis for the LinearDML estimator assuming that its assumption on data-generating process holds: the true function for $Y$ is partial linear. For computational efficiency, we set <b>cache_values</b> = <b>True</b> in `fit_params` to cache the results of first stage estimation.\n", "\n", "Parameters used:\n", "\n", "* <b>method_name</b>: Refutation method name <br>\n", "* <b>simulation_method</b>: \"non-parametric-partial-R2\" for non Parametric Sensitivity Analysis. \n", "Note that partial linear sensitivity analysis is automatically chosen if LinearDML estimator is used for estimation. \n", "* **partial_r2_confounder_treatment**: $\\eta^2_{T\\sim U | W}$, Partial R2 of unobserved confounder with treatment conditioned on all observed confounders. \n", "* **partial_r2_confounder_outcome**: $\\eta^2_{Y \\sim U | T, W}$, Partial R2 of unobserved confounder with outcome conditioned on treatment and all observed confounders. " ] }, { "cell_type": "code", "execution_count": null, "id": "2488ccbb", "metadata": {}, "outputs": [], "source": [ "refute = model.refute_estimate(identified_estimand, linear_dml_estimate ,\n", " method_name = \"add_unobserved_common_cause\",\n", " simulation_method = \"non-parametric-partial-R2\",\n", " partial_r2_confounder_treatment = np.arange(0, 0.8, 0.1),\n", " partial_r2_confounder_outcome = np.arange(0, 0.8, 0.1)\n", " )\n", "print(refute)" ] }, { "cell_type": "markdown", "id": "81f1d65b", "metadata": {}, "source": [ "**Intepretation of the plot.** In the above plot, the x-axis shows hypothetical partial R2 values of unobserved confounder(s) with the treatment. The y-axis shows hypothetical partial R2 of unobserved confounder(s) with the outcome. At <x=0,y=0>, the black diamond shows the original estimate (theta_s) without considering the unobserved confounders.\n", "\n", "The contour levels represent *adjusted* lower confidence bound estimate of the effect, which would be obtained if the unobserved confounder(s) had been included in the estimation model. The red contour line is the critical threshold where the adjusted effect goes to zero. Thus, confounders with such strength or stronger are sufficient to reverse the sign of the estimated effect and invalidate the estimate's conclusions. This notion can be quantified by outputting the robustness value." ] }, { "cell_type": "code", "execution_count": null, "id": "52b2e904", "metadata": {}, "outputs": [], "source": [ "refute.RV" ] }, { "cell_type": "markdown", "id": "3524cb07", "metadata": {}, "source": [ "The robustness value measures the minimal equal strength of $\\eta^2_{T\\sim U | W}$ and $\\eta^2_{Y \\sim U | T, W}$ such the bound for the average treatment effect would include zero. It can be between 0 and 1. <br>\n", "A robustness value of 0.45 implies that confounders with $\\eta^2_{T\\sim U | W}$ and $\\eta^2_{Y \\sim U | T, W}$ values less than 0.4 would not be sufficient enough to bring down the estimates to zero. In general, a low robustness value implies that the results can be changed even by the presence of weak confounders whereas a robustness value close to 1 means the treatment effect can handle even strong confounders that may explain all residual variation of the treatment and the outcome." ] }, { "cell_type": "markdown", "id": "a1fbcf48", "metadata": {}, "source": [ "**Benchmarking.** In general, however, providing a plausible range of partial R2 values is difficult. Instead, we can infer the partial R2 of the unobserved confounder as a multiple of the partial R2 of any subset of observed confounders. So now we just need to specify the effect of unobserved confounding as a multiple/fraction of the observed confounding. This process is known as *benchmarking*." ] }, { "cell_type": "markdown", "id": "7a1f4986", "metadata": {}, "source": [ "The relevant arguments for bencmarking are:\n", "- <b>benchmark_common_causes</b>: Names of the observed confounders used to bound the strengths of unobserved confounder<br>\n", "- <b>effect_fraction_on_treatment</b>: Strength of association between unobserved confounder and treatment compared to benchmark confounders<br>\n", "- <b>effect_fraction_on_outcome</b>: Strength of association between unobserved confounder and outcome compared to benchmark confounders<br>" ] }, { "cell_type": "code", "execution_count": null, "id": "85eefe08", "metadata": {}, "outputs": [], "source": [ "refute_bm = model.refute_estimate(identified_estimand, linear_dml_estimate ,\n", " method_name = \"add_unobserved_common_cause\",\n", " simulation_method = \"non-parametric-partial-R2\",\n", " benchmark_common_causes = [\"W1\"],\n", " effect_fraction_on_treatment = 0.2,\n", " effect_fraction_on_outcome = 0.2\n", " )" ] }, { "cell_type": "markdown", "id": "46b54056", "metadata": {}, "source": [ "The red triangle shows the estimated partial-R^2 of a chosen benchmark observed covariate with the treatment and outcome. In the above call, we chose *W1* as the benchmark covariate. Under assumption that the unobserved confounder cannot be stronger in its effect on treatment and outcome than the observed benchmark covariate (*W1*), the above plot shows that the mean estimated effect will reduce after accounting for unobserved confounding, but still remain substantially above zero.\n" ] }, { "cell_type": "markdown", "id": "070f01c6", "metadata": {}, "source": [ "**Plot types**. The default `plot_type` is to show the `lower_confidence_bound` under a significance level . Other possible values for the `plot_type` are:\n", "* `upper_confidence_bound`: preferably used in cases where the unobserved confounder is expected to lower the estimate.\n", "* `lower_ate_bound`: lower (point) estimate for unconfounded average treatment effect without considering the significance level\n", "* `upper_ate_bound`: upper (point) estimate for unconfounded average treatment effect without considering the significance level\n", "* `bias`: the bias of the obtained estimate compared to the true estimate" ] }, { "cell_type": "code", "execution_count": null, "id": "df23a49b", "metadata": {}, "outputs": [], "source": [ "refute_bm.plot(plot_type = \"upper_confidence_bound\")\n", "refute_bm.plot(plot_type = \"bias\")" ] }, { "cell_type": "markdown", "id": "83052508", "metadata": {}, "source": [ "We can also access the benchmarking results as a data frame." ] }, { "cell_type": "code", "execution_count": null, "id": "934eef00", "metadata": {}, "outputs": [], "source": [ "refute_bm.results" ] }, { "cell_type": "markdown", "id": "1fffe64f", "metadata": {}, "source": [ "## II. Sensitivity Analysis for general non-parametric models\n", "We now perform sensitivity analysis without making any assumption on the true data-generating process. The sensitivity still depends on the partial R2 of unobserved confounder with outcome, $\\eta^2_{Y \\sim U | T, W}$, and a similar parameter for the confounder-treatment relationship. However, the computation of bounds is more complicated and requires estimation of a special function known as reisz function. Refer to Chernozhukov et al. for details." ] }, { "cell_type": "code", "execution_count": null, "id": "7cff3837", "metadata": {}, "outputs": [], "source": [ "# Estimate effect using a non-parametric estimator\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "estimate_npar = model.estimate_effect(identified_estimand, \n", " method_name=\"backdoor.econml.dml.KernelDML\",\n", " method_params={\n", " 'init_params': {'model_y':GradientBoostingRegressor(),\n", " 'model_t': GradientBoostingRegressor(), },\n", " 'fit_params': {},\n", " })\n", "print(estimate_npar)" ] }, { "cell_type": "markdown", "id": "5c971de4", "metadata": {}, "source": [ "To do the sensitivity analysis, we now use the same `non-parametric--partial-R2` method, however the estimation of partial R2 will be based on reisz representers. We use `plugin_reisz=True` to specify that we will be using a plugin reisz function estimator (this is faster and available for binary treatments). Otherwise, we can set it to `False` to estimate reisz function using a loss function." ] }, { "cell_type": "code", "execution_count": null, "id": "946e1237", "metadata": { "scrolled": true }, "outputs": [], "source": [ "refute_npar = model.refute_estimate(identified_estimand, estimate_npar,\n", " method_name = \"add_unobserved_common_cause\",\n", " simulation_method = \"non-parametric-partial-R2\",\n", " benchmark_common_causes = [\"W1\"],\n", " effect_fraction_on_treatment = 0.2,\n", " effect_fraction_on_outcome = 0.2,\n", " plugin_reisz=True\n", " )\n", "print(refute_npar)" ] }, { "cell_type": "markdown", "id": "db63007e", "metadata": {}, "source": [ "The plot has the same interpretation as before. We obtain a robustness value of 0.66 compared to robustness value of 0.45 for LinearDML estimator.\n", "\n", "Note that the robustness value changes, even though the point estimates from LinearDML and KernelDML are similar. This is because we made different assumptions on the true data-generating process. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.10 ('dowhy-_zBapv7Q-py3.8')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "vscode": { "interpreter": { "hash": "dcb481ad5d98e2afacd650b2c07afac80a299b7b701b553e333fc82865502500" } } }, "nbformat": 4, "nbformat_minor": 5 }

andresmor-ms

11c4e0dafd6e824eb81ad14262457d954ae61468

affe0952f4aba6845247355c171565510c2c1673

if there's an easy to remove the vscode hash from every notebook commit, that will be nice. I suspect this hash will change with every commit. If not, it is fairly minor and we can ignore.

amit-sharma