AAAI 2020 Tutorial

Representation Learning for Causal Inference
Sheng Li1, Liuyi Yao2, Yaliang Li3, Jing Gao2, Aidong Zhang4
1

University of Georgia, Athens, GA
2
University at Buffalo, Buffalo, NY
3
Alibaba Group, Bellevue, WA
4
University of Virginia, Charlottesville, VA

Feb. 8, 20201

About this Tutorial❏

Schedule❏

2:00 PM - 2:30 PM: Background on Causal Inference (Li)❏2:30 PM - 3:00 PM: Classical Causal Inference Methods (Yao)❏

3:00 PM - 3:30 PM: Subspace Learning for Causal Inference (Li)❏3:30 PM - 3:45 PM: Deep Learning for Causal Inference (Yao)❏

3:45 PM - 4:15 PM: Coffee Break❏

4:15 PM - 4:50 PM: Deep Learning for Causal Inference (Yao)❏

4:50 PM - 5:20 PM: Applications and Conclusions (Li)❏

Website: http://cobweb.cs.uga.edu/~shengli/AAAI20-Causal-Tutorial.html (Slides)❏

A Survey on Causal Inference (02/2020): https://arxiv.org/abs/2002.02770
2

Outline❏ Background on Causal Inference❏ Classical Causal Inference Methods❏ Subspace Learning for Causal Inference❏ Deep Representation Learning for Causal Inference❏ Applications❏ Conclusions and Future Perspectives
3Causality❏ Causality is also referred to as “causation”, or “cause and effect”❏ Causality has been extensively discussed in many ﬁelds, such as
philosophy, psychology, statistics, political science, economics, education,and healthcare

Figure: http://www.causality.inf.ethz.ch/cause-effect.php

4Correlation and Causation❏ Correlation does not imply causation❏

The inability to legitimately deduce a cause-and-effect relationship between
two variables solely on the basis of an observed association or correlation
between them (from Wikipedia)❏ For two correlated events A and B, the possible relations might be: (1) A
causes B, (2) B causes A, (3) A and B are consequences of a common
cause, but do not cause each other, etc.
❏ Example of (3): As ice cream sales increase, the rate of drowning deaths
increases sharply. Therefore, ice cream consumption causes drowning (?)
5

Causal Inference❏ Causal inference is the process of drawing aconclusion about a causal connection basedon the conditions of the occurrence of aneffect❏ It has been a critical research topic across
many domains, such as statistics, computerscience, education, public policy andeconomics, for decades
6Experimental Study vs. Observational Study❏ Experimental Study❏

Randomized Controlled Trial (RCT)❏Assignment of control/treated is random❏

Gold-standard for studying causal relationships❏

Expensive and time-consuming, e.g., A/B testing❏ Observational Study❏

Assignment is NOT random❏

Approaches: graphical causal models, potential outcome framework❏

Simple, eﬃcient and interpretable, e.g., nearest neighobr matching7

Graphical Causal Models❏ Causal graphs are probabilistic graphicalmodels to encode assumptions about thedata-generating process [Pearl, 2009]❏ D-separation allows determining whether thecausal structure implies that two sets ofvariables are independent given a third set❏ Other related approaches: structural equation
modeling (SEM)
An example of DAG[Pearl, 2009] Judea Pearl. Causality. Cambridge University Press, 2009.

8

Potential Outcome Framework (1)❏ Also known as Rubin causal model (RCM), or Neyman–Rubin causal model❏ Unit: A unit is the atomic research object in the causal study❏ Treatment: An action that applies to a unit
In the binary treatment case (i.e., W = 0 or 1), treated group contains units
received treatment W = 1, while control group contains units received
treatment W = 0❏ Outcome: response of units after treatment/control, denoted as Y
❏ Treatment Effect: The change of outcome when applying the different
treatments on the units

9Potential Outcome Framework (2)❏ Potential Outcome: For each unit-treatment pair, the outcome of thattreatment when applied on that unit is the potential outcome. Y(W=w)❏ Observed Outcome: Outcome of treatment that is actually applied. In
binary case,❏ Counterfactual Outcome: Potential outcome of the treatments that theunit had not taken. In binary case,❏ A unit can only take one treatment. Thus, counterfactual outcomes are
not observed, leading to the well-known “missing data” problem[Holland, 1986] P. Holland, "Statistics and causal inference." Journal of the American Statistical Association, 81.396 (1986): 945-960.

10

Potential Outcome Framework (3)❏Treatment Effects can be deﬁned at the population, treated group,
subgroup and individual levels❏

Population Level: Average Treatment Effect (ATE)❏

Treated group: Average Treatment Effect on the Treated Group (ATT)❏

Subgroup: Conditional Average Treatment Effect (CATE)❏

Individual: Individual Treatment Effect (ITE)11

An Illustrative Example❏

Task: Evaluate the treatment effects of several different medications for
one disease, by exploiting the observational data, such as the electronic
health records (EHR)❏

Observational data may include: (1) demographic information ofpatients, (2) speciﬁc medication with the speciﬁc dosage taken bypatients, and (3) the outcome of medical tests❏

Units: patients❏

Treatments: different medications❏

Outcome: recovery, blood test results, or others

12Assumptions❏ Assumption 1: Stable Unit Treatment Value Assumption (SUTVA)
The potential outcomes for any unit do not vary with the treatment assigned toother units, and, for each unit, there are no different forms or versions of eachtreatment level, which lead to different potential outcomes.

❏ This assumption emphasizes that:❏Independence of each units, i.e., there are no interactions between units. In
our example, one patient's outcome will not affect other patients' outcomes❏

Single version for each treatment. For instance, one medicine withdifferent dosages are different treatments under the SUTVA assumption
13

Assumptions❏ Assumption 2: Ignorability
Given the background variable, X, treatment assignment W is independent of
the potential outcomes, i.e.,❏ Following our example, this assumption implies that:❏If two patients have the same background variable X, their potential
outcome should be the same whatever the treatment assignment is.

❏

Analogously, if two patients have the same background variable value,
their treatment assignment mechanism should be same whatever thevalue of potential outcomes they have14

Assumptions❏ Assumption 3: Positivity
For any set of values of X, treatment assignment is not deterministic:❏ If treatment assignment for some values of X is deterministic, theoutcomes of at least one treatment could never be observed. It would beunable and meaningless to estimate causal effects❏ It implies “common support” or “overlap” of treated and control groups❏ The ignorability and the positivity assumptions together are also called
Strong Ignorability or Strongly Ignorable Treatment Assignment
15

General Solution❏ The core problem is: how to estimate the average potential
treated/control outcomes over a speciﬁc group?
❏ One naive solution is to calculate the difference between the averagetreated and control outcomes, i.e.,❏ However, this solution is not reasonable due to the existence ofconfounders

16

Confounders❏ Confounders: Variables that affect both treatment assignment and outcome❏ In the medical example, age is a confounder❏

Age would affect the recovery rate❏

Age would also affect the treatment choice

Simpson's paradox
due to confounder17

Selection Bias
❏ Selection Bias: The distribution of the observed group is not representative
to the group we are interested in❏ Confounder variables affect units'
treatment choices, which leads to theselection bias
❏ Selection bias makes counterfactual
outcome estimation more diﬃcult

18Discussions❏ Causal inference by estimating treatment effects❏ Connections between graphical causal models and potential
outcome framework❏ Main challenges in causal inference from observational data❏

How to handle confounders?

❏

How to deal with selection bias?

19Outline❏ Background on Causal Inference❏ Classical Causal Inference Methods❏ Subspace Learning for Causal Inference❏ Deep Representation Learning for Causal Inference❏ Applications❏ Conclusions and Future Perspectives
20Classical Causal Inference Methods❏ Categorization of Methods❏

Re-weighting methods❏

Stratiﬁcation methods❏

Matching methods❏

Tree-based methods

21

Re-weighting Methods❏ Challenge of Selection Bias: due to different distributions of treatedand control groups❏ Sample re-weighting is a common way to overcome the selection
bias problem❏ Idea: By assigning appropriate weight to each sample in theobservation dataset, a pseudo-population is created on which the
distributions of the treated group and control group are similar

22

Sample Re-weighting Methods❏

Intuition example: Age (Yong/older) as the confounder
Young

Young

Older

W=1
Treated

W=0
control

http://www.rebeccabarter.com/blog/2017-07-05-ip-weighting/After
re-weighting

Older

W=1

W=0

23

Sample Re-weighting Methods❏ Balancing Score: Balancing score b(X) is a general weighting score,
which is the function of covariates X satisfying: W ⫫ x | b(x).
❏Contains all information about treatment assignment❏

Able to approximate the whole population using balancing score❏ One representative method: Propensity Score based Re-weighting❏ Propensity Score: Conditional probability of assignment to aparticular treatment given a vector of observed covariates

24Sample Re-weighting Methods❏ Inverse propensity weighting (IPW)❏ The weight assigned for each unit is:where W is the treatment and e(x) is the propensity score❏ After re-weighting, the IPW estimator of ATE is deﬁned as:❏

Theoretical results show that adjustment for the scalar propensity score is
suﬃcient to remove bias due to all observed covariates.

❏

However, IPW highly relies on the correctness of propensity scores

J. Robins, A. Rotnitzky, and L. Zhao. "Estimation of regression coefficients when some regressors are not always observed." Journal of the American
statistical Association 89.427 (1994): 846-866.

25

Sample Re-weighting Methods❏ Doubly Robust Estimator (DR) or Augmented IPW❏ It combines the propensity score weighting with the outcome
regression
Potential confounders: x

Propensity scorebased model

Treatment: w

Outcome regression
model: y = m(w, x)

Outcome: y

J. Robins, A. Rotnitzky, and L. Zhao. "Estimation of regression coefficients when some regressors are not always observed." Journal of the American
statistical Association 89.427 (1994): 846-866.

26

Sample Re-weighting Methods❏ Doubly Robust Estimator (DR) or Augmented IPW❏

Unbiased when one of the propensity score or outcome
regression is correct
Observed outcome

Outcome from
regression model

Estimation of treated outcome

Estimation of control outcome

27Sample Re-weighting Methods❏ Doubly Robust Estimator (DR) or Augmented IPW❏

Unbiased when one of the propensity score or outcome
regression is correct

IPW

augmented

IPW

augmented
28

Sample Re-weighting Methods❏ Covariate balancing propensity score (CBPS)❏ As propensity score serves as both the probability of being treated andcovariate balancing score, CBPS exploits this dual characteristics❏ CBPS estimate the propensity score by solving the following problem:

K. Imai and M. Ratkovic. Covariate balancing propensity score. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(1):243–263
29
2014.

Sample & Covariate Re-weighting❏ Data-Driven Variable Decomposition(D2VD)❏ Assumption: Observed variables can be
decomposed into confounders, adjusted
variables and the irrelevant variables❏ D2VD distinguishes the confounders andadjustment variables, and meanwhile,eliminates the irrelevant variables.
Kuang, Kun, et al. "Treatment effect estimation with data-driven variable decomposition." AAAI’17.

30

Sample & Covariate Re-weighting❏ Data-Driven Variable Decomposition (D2VD)❏ Adjusted outcome is:❏ Adjusted ATE is:31

Sample & Covariate Re-weighting❏ Data-Driven Variable Decomposition (D2VD)
separating confounders X
separating the adjustment variables Z
ATE estimation function

Adjusted ATE

Propensity score
estimation loss
Hadamard product ensures theseparation of Z and X

32

Sample & Covariate Re-weighting❏ Differentiated Confounder Balancing (DCB)❏ DCB selects, differentiates confounders to balance the distribution.
❏ DCB balances the distribution by re-weighting both the sample andthe confounders.
W: sample weight
confounder weight
Factualloss

Kuang, Kun, et al. "Estimating treatment effect in the wild via differentiated confounder balancing." Proceedings of the 23rd ACM SIGKDD International
Conference on Knowledge Discovery and Data Mining. 2017.
33

Summary of Re-weighting Methods

34Classical Causal Inference Methods❏ Categorization of Methods❏

Re-weighting methods❏

Stratiﬁcation methods❏

Matching methods❏

Tree-based methods

35Stratiﬁcation❏ Stratiﬁcation adjusts the selection bias by splitting the entire group
into subgroups, where within each subgroup, the treated group andthe control group are similar under some measurements❏ Stratiﬁcation is also named as subclassiﬁcation or blocking❏ ATE for stratiﬁcation is estimated as
j-th block36

Classical Causal Inference Methods❏ Categorization of Methods❏

Re-weighting methods❏

Stratiﬁcation methods❏

Matching methods❏

Tree-based methods

37

Matching❏ Matching methods estimate the counterfactuals and meanwhile
reduce the estimation bias brought by the confounders❏ Potential outcomes of the i-th unit estimated by matching are:

Where J(i) is the matched neighbors of unit i in the opposite
treatment group38

Matching❏ Distance Metrics for Matching❏ Original Data Space❏ Euclidean distance❏ Mahalanobis distance❏ Transformed Feature Space❏ Propensity score based transformation❏ Other transformations (e.g., prognosis score)39

Matching❏ Propensity Score Matching (PSM)❏

Propensity scores denote conditional probability of assignment
to a particular treatment given a vector of observed covariates.

❏

Based on propensity scores, the distance between two units is❏

Alternatively, linear propensity score based distance metric

P. Rosenbaum, and D. Rubin. "The central role of the propensity score in observational studies for causal effects." Biometrika 70.1 (1983): 41-55.

40

Matching❏ Choosing Matching Algorithm❏

Nearest Neighbors❏

Caliper❏

Stratiﬁcation❏

Kernels❏ Variable Selection❏

The more, the better?

❏

Post-treatment variables
41

Matching❏ Summary of Matching Methods

42Classical Causal Inference Methods❏ Categorization of Methods❏

Re-weighting methods❏

Stratiﬁcation methods❏

Matching methods❏

Tree-based methods

43Tree-based Methods❏ Bayesian Additive Regression Trees (BART)❏A Bayesian “sum-of-trees” model❏Nonparametric Bayesian regression model

Hill, Jennifer L. "Bayesian nonparametric modeling for causal inference." Journal of Computational and Graphical Statistics 20.1 (2011): 217-240.
https://www.slideshare.net/SAMSI_Info/mums-bayesian-fiducial-and-frequentist-conference-multiscale-analysis-of-bart-veronika-rockova-april-29-201944

Tree-based Methods❏ Bayesian Additive Regression Trees (BART) Formulation:❏

T denotes a binary tree (with node decision rules and terminal
nodes), M denotes parameters. The mode is:

Example of single tree:

45Tree-based Methods❏ Advantages of BART:❏

Easy to implement. Less requirement for parameter tuning❏

Posterior can provide uncertainty of the estimation❏

BART can deal with a mass of predictors and handle continuous
treatment variables and missing data46

Tree-based Methods❏ Classiﬁcation And Regression Trees (CART)❏

Recursively partition the data space❏

Fit a simple prediction model for each partition❏

Represent every partitioning as a decision tree

❏ Leaf speciﬁc effect:

A speciﬁc leaf node47

Tree-based Methods❏ Causal Forests❏

Single tree is noisy -> using forest❏

It is based on Breiman's random forest algorithm❏

Trees and forests help ﬁnd neighbors adaptively❏

Extended to multiple treatments

S. Wager, and S. Athey. "Estimation and inference of heterogeneous treatment effects using random forests." Journal of the American Statistical
Association 113.523 (2018): 1228-1242.
48

Tree-based Methods❏ Causal Forest:❏

I

J

Single tree as the Double sample
tree❏

Grow a tree

Split the sample into I
samples and J samples❏

Goal: estimate the outcome

Estimate
leaf-speciﬁc
effectAdvantage:❏

Can estimate CATE❏

Consistent to true CATE❏

Nice Asymptotic properties

49

Tree-based Methods❏ Causal Forest:❏

Single tree as the propensity tree❏

Goal: estimate the treatment
assignment W❏

D

Grow a tree

Use full samples
Each leaf nodeat least kobservations

50

Summary❏ Classical Causal Inference Methods❏

Simple methods with theoretical guarantee❏

May not be suﬃcient to handle high dimension data

51

Outline❏ Background on Causal Inference❏ Classical Causal Inference Methods❏ Subspace Learning for Causal Inference❏ Deep Representation Learning for Causal Inference❏ Applications❏ Conclusions and Future Perspectives
52

Subspace Learning❏ Goal: Learning low-dimensional subspaces for dimensionality reduction❏ Representative subspace learning methods include: principal component
analysis (PCA), locality preserving projections (LPP), canonicalcorrelation analysis (CCA), etc.

Figure: https://medium.com/@TheDataGyan/dimensionality-reduction-with-pca-and-t-sne-in-r-2715683819

53

Subspace Learning for Causal Inference❏ Motivation: Matching in the original data space is simple andﬂexible, but it could be misled by variables that do not affect theoutcome. To address this issue, matching could be performed insubspaces instead.
❏ Methods❏

Random Subspaces❏

Informative Subspace❏

Balanced and Nonlinear Subspace
54

Recap: Nearest Neighbor Matching❏ For a treated unit i, nearest neighbor matching (NNM) ﬁnds its
nearest neighbor in control group in terms of covariates.
❏ NNM usually uses metrics such as Euclidean distance andMahalanobis distance.
❏ NNM has diﬃculty in dealing with a large number of covariates. Also,
bias of NNM increases with with the dimensionality of data at a rateO(N-1/d) [Abadie and Imbens, 2006]

A. Abadie and G. Imbens. "Large sample properties of matching estimators for average treatment effects." Econometrica 74.1 (2006): 235-267.

55

NNM with Random Subspaces❏ Motivation❏

Dimension reduction, to soften the dependence of bias to dimension❏

Linear projection, to deal with ‘big data’❏ Johnson-Lindenstrauss (JL) Lemma
Project data to a randomly generated subspace while preserving original distances
between points [Johnson and Lindenstrauss, 1984]

S. Li, N. Vlassis, J. Kawale, Y. Fu. “Matching via Dimensionality Reduction for Estimation of Treatment Effects in Digital Marketing Campaigns”. IJCAI 2016. 56

NNM with Random Subspaces❏ Randomized Nearest Neighbor Matching (RNNM)

TreatmentGroup
Choose K via JL
Lemma
ControlGroup

RandomProjection I

NNM &
ATT1

RandomProjection 2

NNM &
ATT2

…

…

RandomProjection m

NNM &
ATTm

Medianof ATT

57

NNM with Random Subspaces❏ Experiments on Synthetic Dataset❏

1,000 samples, 200 features❏

True outcomes are determined by aset of basis functions❏

Simulated outcomes are drawn from anormal distribution❏

Ground Truth of ATT is 1❏

Metric: average of mean square error(MSE) over 1,000 simulations
58

NNM with Random Subspaces❏ Experiments on Marketing Dataset❏

Email Campaigns: sending two types of promotional emails to two groupsof customers separately❏

1.2 million units in control group, and 0.8 million units in treated group. 209
dimensional features. Outcome: open or click emails

59

NNM with Random Subspaces❏ Experiments on Marketing Dataset: Semi-synthetic Settings❏

Generate a pseudo-treated population from the control group❏

True causal effect is 0

JL bound: log(3000)=860

Informative Subspace Learning❏ Hilbert-Schmidt Independence Criterion (HSIC) based NNM❏ HSIC-NNM learns two linear projections for control outcome
estimation task and treated outcome estimation task separately❏ It maximizes nonlinear dependency between the projected subspace
and the outcome bywhere XwMw is the transformed subspace, YwF is the observed control/ treatedoutcome, and R denotes the regularization term
Y. Chang, J. Dy. “Informative Subspace Learning for Counterfactual Inference”. AAAI 2017.

61

Informative Subspace Learning❏ Experiments on IHDP Dataset❏

Source: Collected by Infant Health and Development Program Treatment group❏

Samples: 24 Covariates; 747 samples (608 control units and 139 treated units)❏

Outcomes: Simulated using covariates and treatment information

62

Nonlinear and Balanced Subspace Learning❏ Challenges❏

Bias increases with the dimension of data❏

Complex & unbalanced distributions of high-dimensional covariates❏ Our Solution❏

Convert counterfactual prediction to a multi-class classiﬁcation problem withpseudo labels❏

Ordinal scatter discrepancy criterion to extract nonlinear representations❏

Maximum mean discrepancy criterion to learn balanced representations

S. Li, and Y. Fu. “Matching on balanced nonlinear representations for treatment effects estimation”. NIPS 2017.

63

Nonlinear and Balanced Subspace Learning❏ Objective Function

P is the learned nonlinear projection❏ It can be solved with a closed-form solution

64Nonlinear and Balanced Subspace Learning❏ Experiments on Synthetic Dataset❏

1,000 samples, 200 features❏

True outcomes are determined by aset of basis functions❏

Simulated outcomes are drawn from anormal distribution❏

Ground Truth of ATT is 1❏

Metric: average of mean square error(MSE) over 1,000 simulations
65

Nonlinear and Balanced Subspace Learning❏ Experiments on IHDP Dataset❏

Source: Collected by the Infant Health andDevelopment Program Treatment group: allchildren with non-white mothers.

❏

Samples: 24 Covariates; 747 samples (608control units and 139 treated units)❏

Outcomes: Simulated using covariates andtreatment information❏

Metric: Error in ATT as evaluation metric66

Nonlinear and Balanced Subspace Learning❏ Experiments on LaLonda Dataset❏

Source: Collected by a randomized study of ajob training program❏

Treatment group: 297 units who participatedin the training program❏

Control group: 2,915 units from surveys andother studies❏

Outcome: earnings in 1978 Ground truth of
ATT is $886 with a standard error of $448
67

Summary❏ Subspace Learning for Causal Inference❏(+) Most methods are highly eﬃcient owing to their closed-form
solutions❏(-) Subspace learning methods usually have strong assumptions
on underlying data distributions❏(-) They are usually combined with Matching estimators, but are
not capable of estimating counterfactuals directly

68Outline❏ Background on Causal Inference❏ Classical Causal Inference Methods❏ Subspace Learning for Causal Inference❏ Deep Representation Learning for Causal Inference❏ Applications❏ Conclusions and Future Perspectives
69

Deep Representation Learning❏

Deep learning architecture is composed of an input layer, hidden layers, and an
output layer❏

The output of each intermediate layer can be viewed as a representation of
the original input data❏

Ability to deliver high-quality features and enhanced learning performance❏

Examples: Feed forward NN, CNN, Auto Encoder, VAE, GAN, etc.

70

Deep Representation Learning for Causal Inference❏ Balanced representation learning❏ Local similarity preserving based methods❏ Deep Generative model based methods

71

Balanced Representation Learning❏ Motivation❏

Counterfactual inference <-> Domain adaptation

Control
Treated72

Balanced Representation Learning❏ Theoretical background❏The expected error of estimating ITE:

Expected supervised learning
generalization error

Distance between the learned
representations73

Balanced Representation Learning❏ Balancing the two groups in the latent space74Balanced Representation Learning❏ BNN/TARNet❏ Objective Function

Factual loss

Discrepancy

F. Johansson, U. Shalit, and D. Sontag. "Learning representations for counterfactual inference." International conference on machine learning. 2016.

75

Balanced Representation Learning❏ Counterfactual Regression❏ Objective Function

Factual loss

Discrepancy

U. Shalit, F. Johansson, and D. Sontag. "Estimating individual treatment effect: generalization bounds and algorithms." Proceedings of the 34th
International Conference on Machine Learning-Volume 70. JMLR. org, 2017.

76

Balanced Representation Learning
BNN/TARNET, CFR Experiments❏

Experiment on IHDP and Jobs dataset (Lalonde dataset)❏

Evaluation metric:❏❏

IHDP dataset:❏

For ITE: Precision in Estimation of Heterogeneous Effect (PEHE)❏For ATE: absolute error of ATE

Jobs dataset:❏

For ITE: Policy risk. The average loss in value when treating according to
the policy implied by an ITE estimator.

❏

For ATT: absolute error of ATT

77

Balanced Representation Learning❏

Within-sample: Estimate the ITE of
the units whose outcome of one
treatment is observed❏ Training + Validation sets78

Balanced Representation Learning❏

Out-of-sample: Estimate the ITE of
the units with no observed outcome❏❏

Test set

Example: a new patient arrives andthe goal is to select the best possible
treatment

79Local similarity preserving based methods❏ Motivation: The latent space should encode:❏

The distribution in latent space is balanced❏

The similarity order information in X (because the performanceof KNN is good)❏For different data points, the strength of similarity should be
different80Local similarity preserving based methods❏

Toy Example

81

SITE
❏ Idea: Using triplet loss to preserve the local similarity❏ Objective Function:
L. Yao, et al. "Representation learning for treatment effect estimation from observational data." NeurIPS 2018.

82

SITE
❏

Triplet pair selection❏

si is the propensity score, which is the probability that a unit is in the treated group❏

Propensity score can reﬂect the relative location of units in the original space

83

SITE
❏

Position-Dependent Deep Metric(PDDM):❏ The PDDM component
measures the local similarityof two units based on theirrelative and absolute
positions in the latent space❏

Middle Point Distance Minimization(MPDM):❏ Makes two mid-points close toeach other❏ The MPDM balances the
distribution in the latent space

84

SITE
Experiment on Twins datasets:❏ Dataset:❏

Source: the data of twins birth in the❏

Evaluation Metric:❏

AUC on outcome estimation

USA between 1989-1991❏

Samples: Total 11,400 twins pairs with30 features relating to the parents, thepregnancy and the birth❏

Treatment group: heavier twin;❏

Control group: light twin❏

Outcome: 1-year mortality
85

SITE: Experiments

Experiment on IHDP and Jobs dataset
86

ACE❏ An improvement of SITE:❏ SITE only considers the similarity of extreme cases❏ SITE requires that the underlying data are spherically distributed
when calculating the group distance❏ ACE❏ Goal:❏ preserve the ﬁne-grained similarity information❏ Obtain balanced distribution in the latent representation

Yao, Liuyi, et al. "ACE: Adaptively Similarity-Preserved Representation Learning for Individual Treatment Effect Estimation." 2019 IEEE International
Conference on Data Mining (ICDM). IEEE, 2019.

87

ACE
Approach: Imposing Balancing & Adaptive-similarity preserving regularization(BAS) on the representation R:❏ Balancing: control/treated group distance minimization in the representation
space❏ Adaptive Similarity Preserving❏ Explores all the pairwise similarity❏ Adaptively preserves the importantsimilarity information

88

ACE
Balancing & Adaptive-similarity preserving regularization (BAS) regularization❏: Group Distance between treated/control group in the representation space❏: Adaptive Similarity Preserving loss → Measure the similarity loss after representation
learning by KL-divergence:

Similarity between i and j in
the original space❏S(. , .) adaptive similarity measure score based on propensity score

Similarity between i and j in thelatent space

Similarity preserving strength

relative distance within the pair

ACE
Experiment on IHDP, Jobs and Twins datasets

90Causal Inference with Text Covariates❏

Challenge: Text covariates contain rich information❏ some textual covariates -> nearly instrumental variables:❏ very predictive to the treatment assignment might not be that predictive to theoutcome.

T

❏

❏

T

Existing work [Pearl, 2012; Wooldridge, 2016] has shown：❏ Conditioning on the nearly instrumental variables tends to amplify the bias in theanalysis of treatment effects.
Requires to ﬁlter out such the nearly instrumental variables!

[Pearl, 2012] Judea Pearl. On a class of bias-amplifying variables that endanger effect estimates. arXiv preprint arXiv:1203.3503, 2012.
[Wooldridge, 2016] Jeffrey M Wooldridge. Should instrumental variables be used as matching variables? Research in Economics, 70(2):232–237, 2016.

91

Causal Inference with Text Covariates❏❏

Learning the latent representation❏

Filter the information of near-instrument variables (W-related discriminator)❏

Conditional treatment-adversarial based method: CTAM

Perform matching on learned representation

L. Yao, S. Li, Y. Li, H. Xue, J. Gao, and A. Zhang. On the estimation of treatment effect with text covariates. IJCAI’1992

Causal Inference with Text Covariates❏❏

Conditional Treatment Discriminator❏ Input: representation Z & the
potential outcome Y❏ Output: the treatment that the unit
received. (0 or 1)
Mini-max Game
❏ The representation learner aims tofool the Conditional Treatment
Discriminator❏ Filter out the information related to
the near instrumental variables
93

Causal Inference with Text Covariates
Experiment on News datasets:❏ Dataset:❏

Source: NY Times corpus❏

Samples: 5000 news items❏

Treated group: viewed on mobile❏

Control group: viewed on desktop❏

Outcome: readers experience

94

VAE for Causal Inference❏ Hidden confounder:
Outcome: mortality

noisy proxies of Z: incomein the last year and place ofresidence

Treatment: medication

Hidden confounder: socio-economic status
95

VAE for Causal Inference❏

CEVAE❏ Requirements: many proxies are available❏ Estimation of a latent-variable model using VAE❏ Discover the hidden confounders❏ Infer how the hidden confounders affecttreatment and outcome❏ Advantages:❏ Weaker assumptions about the data generatingprocess and the structure of the hidden
confounders
96

VAE for Causal Inference❏

CEVAE:

Louizos, Christos, et al. "Causal effect inference with deep latent-variable models." Advances in Neural Information Processing Systems. 2017.
97

VAE for Causal Inference❏

Experiment on IHDP and Jobs datasets:
IHDP

Jobs

98

GANITE❏❏

Motivation❏ Factual outcome -> observed labels
Counterfactual outcome -> missing labels❏ Capture the uncertainty in the counterfactual distributions by attempting
to learn them using a GAN.
Framework: a combination of two GANs
❏ Counterfactual Block:❏ Input: the data with missing labels❏ Goal: estimate the counterfactual outcome❏ Output: the complete data
❏ ITE Block❏ A standard GAN❏ Input: the complete data from counterfactual block

Yoon, Jinsung, James Jordon, and Mihaela van der Schaar. "GANITE: Estimation of individualized treatment effects using generative adversarial
nets." (2018).

99

GANITE100

GANITE❏Counterfactual Block:❏ Counterfactual Generator: generate counterfactual outcomes❏ Counterfactual Discriminator: distinguish which is the factual
outcome given the combined vector of factual outcome andgenerated counterfactual outcome❏

Output of counterfactual Block:❏ Complete dataset (X, T, factual outcome, generated counterfactual
outcome)101

GANITE102GANITEITE Block:❏

ITE Generator: inferring the potential outcomes of the individual
based on the complete dataset in a supervised way❏

ITE discriminator:❏ A Standard conditional GAN discriminator.
❏ Distinguish the potential outcomes from the complete
dataset or the ITE generator

103

GANITE
Experiment on datasetswith binary treatment.
❏

Datasets: IHDP,
Twins, and Jobs
dataset104

GANITE
Experiment on datasets withmultiple treatment.
❏ Datasets: constructed fromoriginal Twins dataset❏ 4 treatments:t = 1: lower weight, female sex
t = 2: lower weight, male sex
t = 3: higher weight, female sex
t = 4: higher weight, male sex❏ Evaluation metric:
mean-squared error on
outcomes:

105

Summary❏ Deep Representation Learning for Causal Inference❏

Balanced representation learning❏

Capture the uncertainty in the distribution ofcounterfactual/unobserved confounders❏

Drawbacks:❏ Some methods lack theoretical guarantee❏ Require large samples to train

106

Outline❏ Background on Causal Inference❏ Classical Causal Inference Methods❏ Subspace Learning for Causal Inference❏ Deep Representation Learning for Causal Inference❏ Applications❏ Conclusions and Future Perspectives
107Applications
Real-world applications fall into mainly three directions.

Decision Evaluation
Selection Bias HandlingCounterfactual Estimation108

Applications
Online Advertising
Decision Evaluation

Email Marketing

Selection Bias Handling

Recommendation

Counterfactual Estimation

Health Care
Education
109

Online Advertising

Decision Evaluation

A new ad increases the clicks?

A new campaign increases sales?

Randomized experiments ?

Estimating the ad effect from observational data110

Online Advertising

Selection Bias Handling

Existing selection
mechanism

Display events

Non-display events

Distribution discrepancy

111

Email Marketing❏

Decision Evaluation

Target potential customers andincrease revenue❏

Choose between two designs ofpromotional email (i.e.,treatments)❏

Choose between two options ofemail subjects

112

Recommender System

Recommends an item
Users

Recommender
SystemUnit
Applies a speciﬁc treatment

113

Health Care
Goal: Learning the optimal per-patient treatment rules.

When the effect of different
available medicines can be
estimated

Try medicine B
on patient 1?

The effect ofusing medicine A
on patient 2?

Doctors can give a better prescription accordingly.

114

Education
By comparing the outcome of different teaching methods on the student
population, a better teaching method can be decided.

The effect of teaching A inthe classroom is better,
while teaching B, the online
class is better.

A

A

B

B

115

Resources❏

Available Toolboxes for Causal Inference

116Resources❏

Available Source Codes (More links are provided in our survey paper )117

Outline❏ Background on Causal Inference❏ Classical Causal Inference Methods❏ Subspace Learning for Causal Inference❏ Deep Representation Learning for Causal Inference❏ Applications❏ Conclusions and Future Perspectives
118

Conclusions❏ Challenges in causal inference❏ Connections between traditional machine learning problems andcausal inference problems❏ Subspace learning approaches for causal inference❏ Deep representation learning approaches for causal inference❏ Domain applications

119

Future Directions
Modeling and Theoretical Study❏ Add or relax assumptions in causal inference models, e.g., how tomodel causal interactions❏ Develop formal connections between different causal models❏ “Machine learning for causal inference” and “Causal inference formachine learning”❏ Equip machine learning models with common sense for better
causal inference❏ Causality-assisted trustworthy learning (e.g., explainability, fairness)120

Future Directions
Application and Evaluation❏ Generalized interpretation of “treatment” and “potential outcome” inmore domain applications❏ Integration of (partial) experimental study and observational study❏ Extensible causal models for multi-modal data
❏ Create benchmarks with real-world data for evaluation purposes, aswell as performance metrics

121Thank you!
Contact: Sheng Li <sheng.li@uga.edu>, Liuyi Yao <liuyiyao@buffalo.edu>❏

Website: http://cobweb.cs.uga.edu/~shengli/AAAI20-Causal-Tutorial.html (Slides)❏

A Survey on Causal Inference (Feb., 2020): https://arxiv.org/abs/2002.02770

122