Lasso linear model with iterative fitting along a regularization path.
See glossary entry for cross-validation estimator.
The best model is selected by cross-validation.
The optimization objective for Lasso is:
Read more in the User Guide.
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.
Number of alphas along the regularization path.
List of alphas where to compute the models. If None alphas are set automatically.
Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
The maximum number of iterations.
The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.
If True, X will be copied; else, it may be overwritten.
Determines the cross-validation splitting strategy. Possible inputs for cv are:
For int/None inputs, KFold is used.
Refer User Guide for the various cross-validation strategies that can be used here.
Changed in version 0.22: cv default value if None changed from 3-fold to 5-fold.
Amount of verbosity.
Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
If positive, restrict regression coefficients to be positive.
The seed of the pseudo random number generator that selects a random feature to update. Used when selection == ‘random’. Pass an int for reproducible output across multiple function calls. See Glossary.
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.
The amount of penalization chosen by cross validation.
Parameter vector (w in the cost function formula).
Independent term in decision function.
Mean square error for the test set on each fold, varying alpha.
The grid of alphas used for fitting.
The dual gap at the end of the optimization for the optimal alpha (alpha_).
Number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.
See also
For an example, see examples/linear_model/plot_lasso_model_selection.py.
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.
fit(X, y)
Fit linear model with coordinate descent.
get_params([deep])
Get parameters for this estimator.
path(*args, **kwargs)
Compute Lasso path with coordinate descent
predict(X)
Predict using the linear model.
score(X, y[, sample_weight])
Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)
Set the parameters of this estimator.
Fit linear model with coordinate descent.
Fit is on grid of alphas and best alpha estimated by cross-validation.
Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output, X can be sparse.
Target values.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Compute Lasso path with coordinate descent
The Lasso optimization function varies for mono and multi-outputs.
For mono-output tasks it is:
For multi-output tasks it is:
Where:
i.e. the sum of norm of each row.
Read more in the User Guide.
Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output then X can be sparse.
Target values
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3
Number of alphas along the regularization path
List of alphas where to compute the models. If None alphas are set automatically
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
If True, X will be copied; else, it may be overwritten.
The initial values of the coefficients.
Amount of verbosity.
whether to return the number of iterations or not.
If set to True, forces coefficients to be positive. (Only allowed when y.ndim == 1).
keyword arguments passed to the coordinate descent solver.
The alphas along the path where models are computed.
Coefficients along the path.
The dual gaps at the end of the optimization for each alpha.
The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha.
See also
For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.
Note that in certain cases, the Lars solver may be significantly faster to implement this functionality. In particular, linear interpolation can be used to retrieve model coefficients between the values output by lars_path
Comparing lasso_path and lars_path with interpolation:
Predict using the linear model.
Samples.
Returns predicted values.
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.
Combine predictors using stacking
Model-based and sequential feature selection
Lasso model selection: Cross-Validation / AIC / BIC
Common pitfalls in interpretation of coefficients of linear models
Cross-validation on diabetes Dataset Exercise


Fit linear model with coordinate descent.
Fit is on grid of alphas and best alpha estimated by cross-validation.
Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output, X can be sparse.
Target values.


Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.


Compute Lasso path with coordinate descent
The Lasso optimization function varies for mono and multi-outputs.
For mono-output tasks it is:
For multi-output tasks it is:
Where:
i.e. the sum of norm of each row.
Read more in the User Guide.
Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output then X can be sparse.
Target values
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3
Number of alphas along the regularization path
List of alphas where to compute the models. If None alphas are set automatically
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
If True, X will be copied; else, it may be overwritten.
The initial values of the coefficients.
Amount of verbosity.
whether to return the number of iterations or not.
If set to True, forces coefficients to be positive. (Only allowed when y.ndim == 1).
keyword arguments passed to the coordinate descent solver.
The alphas along the path where models are computed.
Coefficients along the path.
The dual gaps at the end of the optimization for each alpha.
The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha.
See also
For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.
Note that in certain cases, the Lars solver may be significantly faster to implement this functionality. In particular, linear interpolation can be used to retrieve model coefficients between the values output by lars_path
Comparing lasso_path and lars_path with interpolation:


Predict using the linear model.
Samples.
Returns predicted values.


Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).


Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.


Lasso model fit with Least Angle Regression a.k.a. Lars
It is a Linear Model trained with an L1 prior as regularizer.
The optimization objective for Lasso is:
Read more in the User Guide.
Constant that multiplies the penalty term. Defaults to 1.0. alpha = 0 is equivalent to an ordinary least square, solved by LinearRegression. For numerical reasons, using alpha = 0 with the LassoLars object is not advised and you should prefer the LinearRegression object.
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
Sets the verbosity amount.
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
Maximum number of iterations to perform.
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the tol parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.
If True, X will be copied; else, it may be overwritten.
If True the full path is stored in the coef_path_ attribute. If you compute the solution for a large problem or many targets, setting fit_path to False will lead to a speedup, especially with a small alpha.
Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients will not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (alphas_[alphas_ >
0.].min() when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator.
Upper bound on a uniform noise parameter to be added to the y values, to satisfy the model’s assumption of one-at-a-time computations. Might help with stability.
New in version 0.23.
Determines random number generation for jittering. Pass an int for reproducible output across multiple function calls. See Glossary. Ignored if jitter is None.
New in version 0.23.
Maximum of covariances (in absolute value) at each iteration. n_alphas is either max_iter, n_features or the number of nodes in the path with alpha >= alpha_min, whichever is smaller. If this is a list of array-like, the length of the outer list is n_targets.
Indices of active variables at the end of the path. If this is a list of list, the length of the outer list is n_targets.
If a list is passed it’s expected to be one of n_targets such arrays. The varying values of the coefficients along the path. It is not present if the fit_path parameter is False. If this is a list of array-like, the length of the outer list is n_targets.
Parameter vector (w in the formulation formula).
Independent term in decision function.
The number of iterations taken by lars_path to find the grid of alphas for each target.
See also
fit(X, y[, Xy])
Fit the model using X, y as training data.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict using the linear model.
score(X, y[, sample_weight])
Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)
Set the parameters of this estimator.
Fit the model using X, y as training data.
Training data.
Target values.
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
returns an instance of self.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict using the linear model.
Samples.
Returns predicted values.
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.


Fit the model using X, y as training data.
Training data.
Target values.
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
returns an instance of self.


Cross-validated Lasso, using the LARS algorithm.
See glossary entry for cross-validation estimator.
The optimization objective for Lasso is:
Read more in the User Guide.
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
Sets the verbosity amount.
Maximum number of iterations to perform.
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix cannot be passed as argument since we will use only subsets of X.
Determines the cross-validation splitting strategy. Possible inputs for cv are:
For integer/None inputs, KFold is used.
Refer User Guide for the various cross-validation strategies that can be used here.
Changed in version 0.22: cv default value if None changed from 3-fold to 5-fold.
The maximum number of points on the path used to compute the residuals in the cross-validation
Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the tol parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.
If True, X will be copied; else, it may be overwritten.
Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients do not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (alphas_[alphas_ >
0.].min() when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator. As a consequence using LassoLarsCV only makes sense for problems where a sparse solution is expected and/or reached.
parameter vector (w in the formulation formula)
independent term in decision function.
the varying values of the coefficients along the path
the estimated regularization parameter alpha
the different values of alpha along the path
all the values of alpha along the path for the different folds
the mean square error on left-out for each fold along the path (alpha values given by cv_alphas)
the number of iterations run by Lars with the optimal alpha.
Indices of active variables at the end of the path.
See also
The object solves the same problem as the LassoCV object. However, unlike the LassoCV, it find the relevant alphas values by itself. In general, because of this property, it will be more stable. However, it is more fragile to heavily multicollinear datasets.
It is more efficient than the LassoCV if only a small number of features are selected compared to the total number, for instance if there are very few samples compared to the number of features.
fit(X, y)
Fit the model using X, y as training data.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict using the linear model.
score(X, y[, sample_weight])
Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)
Set the parameters of this estimator.
Fit the model using X, y as training data.
Training data.
Target values.
returns an instance of self.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict using the linear model.
Samples.
Returns predicted values.
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.


Cross-validated Lasso, using the LARS algorithm.
See glossary entry for cross-validation estimator.
The optimization objective for Lasso is:
Read more in the User Guide.
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
Sets the verbosity amount.
Maximum number of iterations to perform.
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix cannot be passed as argument since we will use only subsets of X.
Determines the cross-validation splitting strategy. Possible inputs for cv are:
For integer/None inputs, KFold is used.
Refer User Guide for the various cross-validation strategies that can be used here.
Changed in version 0.22: cv default value if None changed from 3-fold to 5-fold.
The maximum number of points on the path used to compute the residuals in the cross-validation
Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the tol parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.
If True, X will be copied; else, it may be overwritten.
Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients do not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (alphas_[alphas_ >
0.].min() when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator. As a consequence using LassoLarsCV only makes sense for problems where a sparse solution is expected and/or reached.
parameter vector (w in the formulation formula)
independent term in decision function.
the varying values of the coefficients along the path
the estimated regularization parameter alpha
the different values of alpha along the path
all the values of alpha along the path for the different folds
the mean square error on left-out for each fold along the path (alpha values given by cv_alphas)
the number of iterations run by Lars with the optimal alpha.
Indices of active variables at the end of the path.
See also
The object solves the same problem as the LassoCV object. However, unlike the LassoCV, it find the relevant alphas values by itself. In general, because of this property, it will be more stable. However, it is more fragile to heavily multicollinear datasets.
It is more efficient than the LassoCV if only a small number of features are selected compared to the total number, for instance if there are very few samples compared to the number of features.
fit(X, y)
Fit the model using X, y as training data.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict using the linear model.
score(X, y[, sample_weight])
Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)
Set the parameters of this estimator.
Fit the model using X, y as training data.
Training data.
Target values.
returns an instance of self.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict using the linear model.
Samples.
Returns predicted values.
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.
Lasso model selection: Cross-Validation / AIC / BIC


Fit the model using X, y as training data.
Training data.
Target values.
returns an instance of self.


Lasso model fit with Lars using BIC or AIC for model selection
The optimization objective for Lasso is:
AIC is the Akaike information criterion and BIC is the Bayes Information criterion. Such criteria are useful to select the value of the regularization parameter by making a trade-off between the goodness of fit and the complexity of the model. A good model should explain well the data while being simple.
Read more in the User Guide.
The type of criterion to use.
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
Sets the verbosity amount.
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
Maximum number of iterations to perform. Can be used for early stopping.
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the tol parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.
If True, X will be copied; else, it may be overwritten.
Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients do not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (alphas_[alphas_ >
0.].min() when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator. As a consequence using LassoLarsIC only makes sense for problems where a sparse solution is expected and/or reached.
parameter vector (w in the formulation formula)
independent term in decision function.
the alpha parameter chosen by the information criterion
Maximum of covariances (in absolute value) at each iteration. n_alphas is either max_iter, n_features or the number of nodes in the path with alpha >= alpha_min, whichever is smaller. If a list, it will be of length n_targets.
number of iterations run by lars_path to find the grid of alphas.
The value of the information criteria (‘aic’, ‘bic’) across all alphas. The alpha which has the smallest information criterion is chosen. This value is larger by a factor of n_samples compared to Eqns. 2.15 and 2.16 in (Zou et al, 2007).
See also
The estimation of the number of degrees of freedom is given by:
“On the degrees of freedom of the lasso” Hui Zou, Trevor Hastie, and Robert Tibshirani Ann. Statist. Volume 35, Number 5 (2007), 2173-2192.
https://en.wikipedia.org/wiki/Akaike_information_criterion https://en.wikipedia.org/wiki/Bayesian_information_criterion
fit(X, y[, copy_X])
Fit the model using X, y as training data.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict using the linear model.
score(X, y[, sample_weight])
Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)
Set the parameters of this estimator.
Fit the model using X, y as training data.
training data.
target values. Will be cast to X’s dtype if necessary
If provided, this parameter will override the choice of copy_X made at instance creation. If True, X will be copied; else, it may be overwritten.
returns an instance of self.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict using the linear model.
Samples.
Returns predicted values.
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.


Lasso model fit with Lars using BIC or AIC for model selection
The optimization objective for Lasso is:
AIC is the Akaike information criterion and BIC is the Bayes Information criterion. Such criteria are useful to select the value of the regularization parameter by making a trade-off between the goodness of fit and the complexity of the model. A good model should explain well the data while being simple.
Read more in the User Guide.
The type of criterion to use.
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
Sets the verbosity amount.
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
Maximum number of iterations to perform. Can be used for early stopping.
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the tol parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.
If True, X will be copied; else, it may be overwritten.
Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients do not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (alphas_[alphas_ >
0.].min() when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator. As a consequence using LassoLarsIC only makes sense for problems where a sparse solution is expected and/or reached.
parameter vector (w in the formulation formula)
independent term in decision function.
the alpha parameter chosen by the information criterion
Maximum of covariances (in absolute value) at each iteration. n_alphas is either max_iter, n_features or the number of nodes in the path with alpha >= alpha_min, whichever is smaller. If a list, it will be of length n_targets.
number of iterations run by lars_path to find the grid of alphas.
The value of the information criteria (‘aic’, ‘bic’) across all alphas. The alpha which has the smallest information criterion is chosen. This value is larger by a factor of n_samples compared to Eqns. 2.15 and 2.16 in (Zou et al, 2007).
See also
The estimation of the number of degrees of freedom is given by:
“On the degrees of freedom of the lasso” Hui Zou, Trevor Hastie, and Robert Tibshirani Ann. Statist. Volume 35, Number 5 (2007), 2173-2192.
https://en.wikipedia.org/wiki/Akaike_information_criterion https://en.wikipedia.org/wiki/Bayesian_information_criterion
fit(X, y[, copy_X])
Fit the model using X, y as training data.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict using the linear model.
score(X, y[, sample_weight])
Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)
Set the parameters of this estimator.
Fit the model using X, y as training data.
training data.
target values. Will be cast to X’s dtype if necessary
If provided, this parameter will override the choice of copy_X made at instance creation. If True, X will be copied; else, it may be overwritten.
returns an instance of self.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict using the linear model.
Samples.
Returns predicted values.
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.
Lasso model selection: Cross-Validation / AIC / BIC


Fit the model using X, y as training data.
training data.
target values. Will be cast to X’s dtype if necessary
If provided, this parameter will override the choice of copy_X made at instance creation. If True, X will be copied; else, it may be overwritten.
returns an instance of self.


Ordinary least squares Linear Regression.
LinearRegression fits a linear model with coefficients w = (w1, …, wp) to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation.
Whether to calculate the intercept for this model. If set to False, no intercept will be used in calculations (i.e. data is expected to be centered).
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
If True, X will be copied; else, it may be overwritten.
The number of jobs to use for the computation. This will only provide speedup for n_targets > 1 and sufficient large problems. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
When set to True, forces the coefficients to be positive. This option is only supported for dense arrays.
New in version 0.24.
Estimated coefficients for the linear regression problem. If multiple targets are passed during the fit (y 2D), this is a 2D array of shape (n_targets, n_features), while if only one target is passed, this is a 1D array of length n_features.
Rank of matrix X. Only available when X is dense.
Singular values of X. Only available when X is dense.
Independent term in the linear model. Set to 0.0 if fit_intercept = False.
See also
Ridge regression addresses some of the problems of Ordinary Least Squares by imposing a penalty on the size of the coefficients with l2 regularization.
The Lasso is a linear model that estimates sparse coefficients with l1 regularization.
Elastic-Net is a linear regression model trained with both l1 and l2 -norm regularization of the coefficients.
From the implementation point of view, this is just plain Ordinary Least Squares (scipy.linalg.lstsq) or Non Negative Least Squares (scipy.optimize.nnls) wrapped as a predictor object.
fit(X, y[, sample_weight])
Fit linear model.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict using the linear model.
score(X, y[, sample_weight])
Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)
Set the parameters of this estimator.
Fit linear model.
Training data
Target values. Will be cast to X’s dtype if necessary
Individual weights for each sample
New in version 0.17: parameter sample_weight support to LinearRegression.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict using the linear model.
Samples.
Returns predicted values.
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.


Ordinary least squares Linear Regression.
LinearRegression fits a linear model with coefficients w = (w1, …, wp) to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation.
Whether to calculate the intercept for this model. If set to False, no intercept will be used in calculations (i.e. data is expected to be centered).
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
If True, X will be copied; else, it may be overwritten.
The number of jobs to use for the computation. This will only provide speedup for n_targets > 1 and sufficient large problems. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
When set to True, forces the coefficients to be positive. This option is only supported for dense arrays.
New in version 0.24.
Estimated coefficients for the linear regression problem. If multiple targets are passed during the fit (y 2D), this is a 2D array of shape (n_targets, n_features), while if only one target is passed, this is a 1D array of length n_features.
Rank of matrix X. Only available when X is dense.
Singular values of X. Only available when X is dense.
Independent term in the linear model. Set to 0.0 if fit_intercept = False.
See also
Ridge regression addresses some of the problems of Ordinary Least Squares by imposing a penalty on the size of the coefficients with l2 regularization.
The Lasso is a linear model that estimates sparse coefficients with l1 regularization.
Elastic-Net is a linear regression model trained with both l1 and l2 -norm regularization of the coefficients.
From the implementation point of view, this is just plain Ordinary Least Squares (scipy.linalg.lstsq) or Non Negative Least Squares (scipy.optimize.nnls) wrapped as a predictor object.
fit(X, y[, sample_weight])
Fit linear model.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict using the linear model.
score(X, y[, sample_weight])
Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)
Set the parameters of this estimator.
Fit linear model.
Training data
Target values. Will be cast to X’s dtype if necessary
Individual weights for each sample
New in version 0.17: parameter sample_weight support to LinearRegression.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict using the linear model.
Samples.
Returns predicted values.
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.
Principal Component Regression vs Partial Least Squares Regression
Plot individual and voting regression predictions
Ordinary Least Squares and Ridge Regression Variance
Logistic function
Non-negative least squares
Linear Regression Example
Robust linear model estimation using RANSAC
Sparsity Example: Fitting only features 1 and 2
Theil-Sen Regression
Robust linear estimator fitting
Automatic Relevance Determination Regression (ARD)
Bayesian Ridge Regression
Isotonic Regression
Face completion with a multi-output estimators
Plotting Cross-Validated Predictions
Underfitting vs. Overfitting
Using KBinsDiscretizer to discretize continuous features


Fit linear model.
Training data
Target values. Will be cast to X’s dtype if necessary
Individual weights for each sample
New in version 0.17: parameter sample_weight support to LinearRegression.


Logistic Regression (aka logit, MaxEnt) classifier.
In the multiclass case, the training algorithm uses the one-vs-rest (OvR) scheme if the ‘multi_class’ option is set to ‘ovr’, and uses the cross-entropy loss if the ‘multi_class’ option is set to ‘multinomial’. (Currently the ‘multinomial’ option is supported only by the ‘lbfgs’, ‘sag’, ‘saga’ and ‘newton-cg’ solvers.)
This class implements regularized logistic regression using the ‘liblinear’ library, ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ solvers. Note that regularization is applied by default. It can handle both dense and sparse input. Use C-ordered arrays or CSR matrices containing 64-bit floats for optimal performance; any other input format will be converted (and copied).
The ‘newton-cg’, ‘sag’, and ‘lbfgs’ solvers support only L2 regularization with primal formulation, or no regularization. The ‘liblinear’ solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty. The Elastic-Net regularization is only supported by the ‘saga’ solver.
Read more in the User Guide.
Used to specify the norm used in the penalization. The ‘newton-cg’, ‘sag’ and ‘lbfgs’ solvers support only l2 penalties. ‘elasticnet’ is only supported by the ‘saga’ solver. If ‘none’ (not supported by the liblinear solver), no regularization is applied.
New in version 0.19: l1 penalty with SAGA solver (allowing ‘multinomial’ + L1)
Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.
Tolerance for stopping criteria.
Inverse of regularization strength; must be a positive float. Like in support vector machines, smaller values specify stronger regularization.
Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function.
Useful only when the solver ‘liblinear’ is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a “synthetic” feature with constant value equal to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic_feature_weight.
Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased.
Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one.
The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y)).
Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.
New in version 0.17: class_weight=’balanced’
Used when solver == ‘sag’, ‘saga’ or ‘liblinear’ to shuffle the data. See Glossary for details.
Algorithm to use in the optimization problem.
Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.
New in version 0.17: Stochastic Average Gradient descent solver.
New in version 0.19: SAGA solver.
Changed in version 0.22: The default solver changed from ‘liblinear’ to ‘lbfgs’ in 0.22.
Maximum number of iterations taken for the solvers to converge.
If the option chosen is ‘ovr’, then a binary problem is fit for each label. For ‘multinomial’ the loss minimised is the multinomial loss fit across the entire probability distribution, even when the data is binary. ‘multinomial’ is unavailable when solver=’liblinear’. ‘auto’ selects ‘ovr’ if the data is binary, or if solver=’liblinear’, and otherwise selects ‘multinomial’.
New in version 0.18: Stochastic Average Gradient descent solver for ‘multinomial’ case.
Changed in version 0.22: Default changed from ‘ovr’ to ‘auto’ in 0.22.
For the liblinear and lbfgs solvers set verbose to any positive number for verbosity.
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. Useless for liblinear solver. See the Glossary.
New in version 0.17: warm_start to support lbfgs, newton-cg, sag, saga solvers.
Number of CPU cores used when parallelizing over classes if multi_class=’ovr’”. This parameter is ignored when the solver is set to ‘liblinear’ regardless of whether ‘multi_class’ is specified or not. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
The Elastic-Net mixing parameter, with 0 <= l1_ratio <= 1. Only used if penalty='elasticnet'. Setting l1_ratio=0 is equivalent to using penalty='l2', while setting l1_ratio=1 is equivalent to using penalty='l1'. For 0 < l1_ratio <1, the penalty is a combination of L1 and L2.
A list of class labels known to the classifier.
Coefficient of the features in the decision function.
coef_ is of shape (1, n_features) when the given problem is binary. In particular, when multi_class='multinomial', coef_ corresponds to outcome 1 (True) and -coef_ corresponds to outcome 0 (False).
Intercept (a.k.a. bias) added to the decision function.
If fit_intercept is set to False, the intercept is set to zero. intercept_ is of shape (1,) when the given problem is binary. In particular, when multi_class='multinomial', intercept_ corresponds to outcome 1 (True) and -intercept_ corresponds to outcome 0 (False).
Actual number of iterations for all classes. If binary or multinomial, it returns only 1 element. For liblinear solver, only the maximum number of iteration across all classes is given.
Changed in version 0.20: In SciPy <= 1.0.0 the number of lbfgs iterations may exceed max_iter. n_iter_ will now report at most max_iter.
See also
Incrementally trained logistic regression (when given the parameter loss="log").
Logistic regression with built-in cross validation.
The underlying C implementation uses a random number generator to select features when fitting the model. It is thus not uncommon, to have slightly different results for the same input data. If that happens, try with a smaller tol parameter.
Predict output may not match that of standalone liblinear in certain cases. See differences from liblinear in the narrative documentation.
Ciyou Zhu, Richard Byrd, Jorge Nocedal and Jose Luis Morales. http://users.iems.northwestern.edu/~nocedal/lbfgsb.html
https://www.csie.ntu.edu.tw/~cjlin/liblinear/
Minimizing Finite Sums with the Stochastic Average Gradient https://hal.inria.fr/hal-00860051/document
SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives https://arxiv.org/abs/1407.0202
methods for logistic regression and maximum entropy models. Machine Learning 85(1-2):41-75. https://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf
decision_function(X)
Predict confidence scores for samples.
densify()
Convert coefficient matrix to dense array format.
fit(X, y[, sample_weight])
Fit the model according to the given training data.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict class labels for samples in X.
predict_log_proba(X)
Predict logarithm of probability estimates.
predict_proba(X)
Probability estimates.
score(X, y[, sample_weight])
Return the mean accuracy on the given test data and labels.
set_params(**params)
Set the parameters of this estimator.
sparsify()
Convert coefficient matrix to sparse format.
Predict confidence scores for samples.
The confidence score for a sample is proportional to the signed distance of that sample to the hyperplane.
Samples.
Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.
Convert coefficient matrix to dense array format.
Converts the coef_ member (back) to a numpy.ndarray. This is the default format of coef_ and is required for fitting, so calling this method is only required on models that have previously been sparsified; otherwise, it is a no-op.
Fitted estimator.
Fit the model according to the given training data.
Training vector, where n_samples is the number of samples and n_features is the number of features.
Target vector relative to X.
Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.
New in version 0.17: sample_weight support to LogisticRegression.
Fitted estimator.
The SAGA solver supports both float64 and float32 bit arrays.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict class labels for samples in X.
Samples.
Predicted class label per sample.
Predict logarithm of probability estimates.
The returned estimates for all classes are ordered by the label of classes.
Vector to be scored, where n_samples is the number of samples and n_features is the number of features.
Returns the log-probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.
Probability estimates.
The returned estimates for all classes are ordered by the label of classes.
For a multi_class problem, if multi_class is set to be “multinomial” the softmax function is used to find the predicted probability of each class. Else use a one-vs-rest approach, i.e calculate the probability of each class assuming it to be positive using the logistic function. and normalize these values across all the classes.
Vector to be scored, where n_samples is the number of samples and n_features is the number of features.
Returns the probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.
Return the mean accuracy on the given test data and labels.
In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.
Test samples.
True labels for X.
Sample weights.
Mean accuracy of self.predict(X) wrt. y.
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.
Convert coefficient matrix to sparse format.
Converts the coef_ member to a scipy.sparse matrix, which for L1-regularized models can be much more memory- and storage-efficient than the usual numpy.ndarray representation.
The intercept_ member is not converted.
Fitted estimator.
For non-sparse models, i.e. when there are not many zeros in coef_, this may actually increase memory usage, so use this method with care. A rule of thumb is that the number of zero elements, which can be computed with (coef_ == 0).sum(), must be more than 50% for this to provide significant benefits.
After calling this method, further fitting with the partial_fit method (if any) will not work until you call densify.


Logistic Regression (aka logit, MaxEnt) classifier.
In the multiclass case, the training algorithm uses the one-vs-rest (OvR) scheme if the ‘multi_class’ option is set to ‘ovr’, and uses the cross-entropy loss if the ‘multi_class’ option is set to ‘multinomial’. (Currently the ‘multinomial’ option is supported only by the ‘lbfgs’, ‘sag’, ‘saga’ and ‘newton-cg’ solvers.)
This class implements regularized logistic regression using the ‘liblinear’ library, ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ solvers. Note that regularization is applied by default. It can handle both dense and sparse input. Use C-ordered arrays or CSR matrices containing 64-bit floats for optimal performance; any other input format will be converted (and copied).
The ‘newton-cg’, ‘sag’, and ‘lbfgs’ solvers support only L2 regularization with primal formulation, or no regularization. The ‘liblinear’ solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty. The Elastic-Net regularization is only supported by the ‘saga’ solver.
Read more in the User Guide.
Used to specify the norm used in the penalization. The ‘newton-cg’, ‘sag’ and ‘lbfgs’ solvers support only l2 penalties. ‘elasticnet’ is only supported by the ‘saga’ solver. If ‘none’ (not supported by the liblinear solver), no regularization is applied.
New in version 0.19: l1 penalty with SAGA solver (allowing ‘multinomial’ + L1)
Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.
Tolerance for stopping criteria.
Inverse of regularization strength; must be a positive float. Like in support vector machines, smaller values specify stronger regularization.
Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function.
Useful only when the solver ‘liblinear’ is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a “synthetic” feature with constant value equal to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic_feature_weight.
Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased.
Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one.
The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y)).
Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.
New in version 0.17: class_weight=’balanced’
Used when solver == ‘sag’, ‘saga’ or ‘liblinear’ to shuffle the data. See Glossary for details.
Algorithm to use in the optimization problem.
Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.
New in version 0.17: Stochastic Average Gradient descent solver.
New in version 0.19: SAGA solver.
Changed in version 0.22: The default solver changed from ‘liblinear’ to ‘lbfgs’ in 0.22.
Maximum number of iterations taken for the solvers to converge.
If the option chosen is ‘ovr’, then a binary problem is fit for each label. For ‘multinomial’ the loss minimised is the multinomial loss fit across the entire probability distribution, even when the data is binary. ‘multinomial’ is unavailable when solver=’liblinear’. ‘auto’ selects ‘ovr’ if the data is binary, or if solver=’liblinear’, and otherwise selects ‘multinomial’.
New in version 0.18: Stochastic Average Gradient descent solver for ‘multinomial’ case.
Changed in version 0.22: Default changed from ‘ovr’ to ‘auto’ in 0.22.
For the liblinear and lbfgs solvers set verbose to any positive number for verbosity.
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. Useless for liblinear solver. See the Glossary.
New in version 0.17: warm_start to support lbfgs, newton-cg, sag, saga solvers.
Number of CPU cores used when parallelizing over classes if multi_class=’ovr’”. This parameter is ignored when the solver is set to ‘liblinear’ regardless of whether ‘multi_class’ is specified or not. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
The Elastic-Net mixing parameter, with 0 <= l1_ratio <= 1. Only used if penalty='elasticnet'. Setting l1_ratio=0 is equivalent to using penalty='l2', while setting l1_ratio=1 is equivalent to using penalty='l1'. For 0 < l1_ratio <1, the penalty is a combination of L1 and L2.
A list of class labels known to the classifier.
Coefficient of the features in the decision function.
coef_ is of shape (1, n_features) when the given problem is binary. In particular, when multi_class='multinomial', coef_ corresponds to outcome 1 (True) and -coef_ corresponds to outcome 0 (False).
Intercept (a.k.a. bias) added to the decision function.
If fit_intercept is set to False, the intercept is set to zero. intercept_ is of shape (1,) when the given problem is binary. In particular, when multi_class='multinomial', intercept_ corresponds to outcome 1 (True) and -intercept_ corresponds to outcome 0 (False).
Actual number of iterations for all classes. If binary or multinomial, it returns only 1 element. For liblinear solver, only the maximum number of iteration across all classes is given.
Changed in version 0.20: In SciPy <= 1.0.0 the number of lbfgs iterations may exceed max_iter. n_iter_ will now report at most max_iter.
See also
Incrementally trained logistic regression (when given the parameter loss="log").
Logistic regression with built-in cross validation.
The underlying C implementation uses a random number generator to select features when fitting the model. It is thus not uncommon, to have slightly different results for the same input data. If that happens, try with a smaller tol parameter.
Predict output may not match that of standalone liblinear in certain cases. See differences from liblinear in the narrative documentation.
Ciyou Zhu, Richard Byrd, Jorge Nocedal and Jose Luis Morales. http://users.iems.northwestern.edu/~nocedal/lbfgsb.html
https://www.csie.ntu.edu.tw/~cjlin/liblinear/
Minimizing Finite Sums with the Stochastic Average Gradient https://hal.inria.fr/hal-00860051/document
SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives https://arxiv.org/abs/1407.0202
methods for logistic regression and maximum entropy models. Machine Learning 85(1-2):41-75. https://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf
decision_function(X)
Predict confidence scores for samples.
densify()
Convert coefficient matrix to dense array format.
fit(X, y[, sample_weight])
Fit the model according to the given training data.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict class labels for samples in X.
predict_log_proba(X)
Predict logarithm of probability estimates.
predict_proba(X)
Probability estimates.
score(X, y[, sample_weight])
Return the mean accuracy on the given test data and labels.
set_params(**params)
Set the parameters of this estimator.
sparsify()
Convert coefficient matrix to sparse format.
Predict confidence scores for samples.
The confidence score for a sample is proportional to the signed distance of that sample to the hyperplane.
Samples.
Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.
Convert coefficient matrix to dense array format.
Converts the coef_ member (back) to a numpy.ndarray. This is the default format of coef_ and is required for fitting, so calling this method is only required on models that have previously been sparsified; otherwise, it is a no-op.
Fitted estimator.
Fit the model according to the given training data.
Training vector, where n_samples is the number of samples and n_features is the number of features.
Target vector relative to X.
Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.
New in version 0.17: sample_weight support to LogisticRegression.
Fitted estimator.
The SAGA solver supports both float64 and float32 bit arrays.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict class labels for samples in X.
Samples.
Predicted class label per sample.
Predict logarithm of probability estimates.
The returned estimates for all classes are ordered by the label of classes.
Vector to be scored, where n_samples is the number of samples and n_features is the number of features.
Returns the log-probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.
Probability estimates.
The returned estimates for all classes are ordered by the label of classes.
For a multi_class problem, if multi_class is set to be “multinomial” the softmax function is used to find the predicted probability of each class. Else use a one-vs-rest approach, i.e calculate the probability of each class assuming it to be positive using the logistic function. and normalize these values across all the classes.
Vector to be scored, where n_samples is the number of samples and n_features is the number of features.
Returns the probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.
Return the mean accuracy on the given test data and labels.
In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.
Test samples.
True labels for X.
Sample weights.
Mean accuracy of self.predict(X) wrt. y.
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.
Convert coefficient matrix to sparse format.
Converts the coef_ member to a scipy.sparse matrix, which for L1-regularized models can be much more memory- and storage-efficient than the usual numpy.ndarray representation.
The intercept_ member is not converted.
Fitted estimator.
For non-sparse models, i.e. when there are not many zeros in coef_, this may actually increase memory usage, so use this method with care. A rule of thumb is that the number of zero elements, which can be computed with (coef_ == 0).sum(), must be more than 50% for this to provide significant benefits.
After calling this method, further fitting with the partial_fit method (if any) will not work until you call densify.
Release Highlights for scikit-learn 0.23
Release Highlights for scikit-learn 0.24
Release Highlights for scikit-learn 0.22
Comparison of Calibration of Classifiers
Probability Calibration curves
Plot classification probability
Plot class probabilities calculated by the VotingClassifier
Feature transformations with ensembles of trees
Logistic function
Regularization path of L1- Logistic Regression
Logistic Regression 3-class Classifier
Comparing various online solvers
MNIST classification using multinomial logistic + L1
Plot multinomial and One-vs-Rest Logistic Regression
L1 Penalty and Sparsity in Logistic Regression
Multiclass sparse logistic regression on 20newgroups
Compact estimator representations
Visualizations with Display Objects
Classifier Chain
Restricted Boltzmann Machine features for digit classification
Pipelining: chaining a PCA and a logistic regression
Column Transformer with Mixed Types
Feature discretization
Digits Classification Exercise


Predict confidence scores for samples.
The confidence score for a sample is proportional to the signed distance of that sample to the hyperplane.
Samples.
Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.


Convert coefficient matrix to dense array format.
Converts the coef_ member (back) to a numpy.ndarray. This is the default format of coef_ and is required for fitting, so calling this method is only required on models that have previously been sparsified; otherwise, it is a no-op.
Fitted estimator.


Fit the model according to the given training data.
Training vector, where n_samples is the number of samples and n_features is the number of features.
Target vector relative to X.
Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.
New in version 0.17: sample_weight support to LogisticRegression.
Fitted estimator.
The SAGA solver supports both float64 and float32 bit arrays.


Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.


Predict class labels for samples in X.
Samples.
Predicted class label per sample.


Predict logarithm of probability estimates.
The returned estimates for all classes are ordered by the label of classes.
Vector to be scored, where n_samples is the number of samples and n_features is the number of features.
Returns the log-probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.


Probability estimates.
The returned estimates for all classes are ordered by the label of classes.
For a multi_class problem, if multi_class is set to be “multinomial” the softmax function is used to find the predicted probability of each class. Else use a one-vs-rest approach, i.e calculate the probability of each class assuming it to be positive using the logistic function. and normalize these values across all the classes.
Vector to be scored, where n_samples is the number of samples and n_features is the number of features.
Returns the probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.


Return the mean accuracy on the given test data and labels.
In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.
Test samples.
True labels for X.
Sample weights.
Mean accuracy of self.predict(X) wrt. y.


Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.


Convert coefficient matrix to sparse format.
Converts the coef_ member to a scipy.sparse matrix, which for L1-regularized models can be much more memory- and storage-efficient than the usual numpy.ndarray representation.
The intercept_ member is not converted.
Fitted estimator.
For non-sparse models, i.e. when there are not many zeros in coef_, this may actually increase memory usage, so use this method with care. A rule of thumb is that the number of zero elements, which can be computed with (coef_ == 0).sum(), must be more than 50% for this to provide significant benefits.
After calling this method, further fitting with the partial_fit method (if any) will not work until you call densify.


Logistic Regression CV (aka logit, MaxEnt) classifier.
See glossary entry for cross-validation estimator.
This class implements logistic regression using liblinear, newton-cg, sag of lbfgs optimizer. The newton-cg, sag and lbfgs solvers support only L2 regularization with primal formulation. The liblinear solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty. Elastic-Net penalty is only supported by the saga solver.
For the grid of Cs values and l1_ratios values, the best hyperparameter is selected by the cross-validator StratifiedKFold, but it can be changed using the cv parameter. The ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ solvers can warm-start the coefficients (see Glossary).
Read more in the User Guide.
Each of the values in Cs describes the inverse of regularization strength. If Cs is as an int, then a grid of Cs values are chosen in a logarithmic scale between 1e-4 and 1e4. Like in support vector machines, smaller values specify stronger regularization.
Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function.
The default cross-validation generator used is Stratified K-Folds. If an integer is provided, then it is the number of folds used. See the module sklearn.model_selection module for the list of possible cross-validation objects.
Changed in version 0.22: cv default value if None changed from 3-fold to 5-fold.
Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.
Used to specify the norm used in the penalization. The ‘newton-cg’, ‘sag’ and ‘lbfgs’ solvers support only l2 penalties. ‘elasticnet’ is only supported by the ‘saga’ solver.
A string (see model evaluation documentation) or a scorer callable object / function with signature scorer(estimator, X, y). For a list of scoring functions that can be used, look at sklearn.metrics. The default scoring option used is ‘accuracy’.
Algorithm to use in the optimization problem.
Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.
New in version 0.17: Stochastic Average Gradient descent solver.
New in version 0.19: SAGA solver.
Tolerance for stopping criteria.
Maximum number of iterations of the optimization algorithm.
Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one.
The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y)).
Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.
New in version 0.17: class_weight == ‘balanced’
Number of CPU cores used during the cross-validation loop. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
For the ‘liblinear’, ‘sag’ and ‘lbfgs’ solvers set verbose to any positive number for verbosity.
If set to True, the scores are averaged across all folds, and the coefs and the C that corresponds to the best score is taken, and a final refit is done using these parameters. Otherwise the coefs, intercepts and C that correspond to the best scores across folds are averaged.
Useful only when the solver ‘liblinear’ is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a “synthetic” feature with constant value equal to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic_feature_weight.
Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased.
If the option chosen is ‘ovr’, then a binary problem is fit for each label. For ‘multinomial’ the loss minimised is the multinomial loss fit across the entire probability distribution, even when the data is binary. ‘multinomial’ is unavailable when solver=’liblinear’. ‘auto’ selects ‘ovr’ if the data is binary, or if solver=’liblinear’, and otherwise selects ‘multinomial’.
New in version 0.18: Stochastic Average Gradient descent solver for ‘multinomial’ case.
Changed in version 0.22: Default changed from ‘ovr’ to ‘auto’ in 0.22.
Used when solver='sag', ‘saga’ or ‘liblinear’ to shuffle the data. Note that this only applies to the solver and not the cross-validation generator. See Glossary for details.
The list of Elastic-Net mixing parameter, with 0 <= l1_ratio <= 1. Only used if penalty='elasticnet'. A value of 0 is equivalent to using penalty='l2', while 1 is equivalent to using penalty='l1'. For 0 < l1_ratio <1, the penalty is a combination of L1 and L2.
A list of class labels known to the classifier.
Coefficient of the features in the decision function.
coef_ is of shape (1, n_features) when the given problem is binary.
Intercept (a.k.a. bias) added to the decision function.
If fit_intercept is set to False, the intercept is set to zero. intercept_ is of shape(1,) when the problem is binary.
Array of C i.e. inverse of regularization parameter values used for cross-validation.
Array of l1_ratios used for cross-validation. If no l1_ratio is used (i.e. penalty is not ‘elasticnet’), this is set to [None]
dict with classes as the keys, and the path of coefficients obtained during cross-validating across each fold and then across each Cs after doing an OvR for the corresponding class as values. If the ‘multi_class’ option is set to ‘multinomial’, then the coefs_paths are the coefficients corresponding to each class. Each dict value has shape (n_folds, n_cs, n_features) or (n_folds, n_cs, n_features + 1) depending on whether the intercept is fit or not. If penalty='elasticnet', the shape is (n_folds, n_cs, n_l1_ratios_, n_features) or (n_folds, n_cs, n_l1_ratios_, n_features + 1).
dict with classes as the keys, and the values as the grid of scores obtained during cross-validating each fold, after doing an OvR for the corresponding class. If the ‘multi_class’ option given is ‘multinomial’ then the same scores are repeated across all classes, since this is the multinomial class. Each dict value has shape (n_folds, n_cs or (n_folds, n_cs, n_l1_ratios) if penalty='elasticnet'.
Array of C that maps to the best scores across every class. If refit is set to False, then for each class, the best C is the average of the C’s that correspond to the best scores for each fold. C_ is of shape(n_classes,) when the problem is binary.
Array of l1_ratio that maps to the best scores across every class. If refit is set to False, then for each class, the best l1_ratio is the average of the l1_ratio’s that correspond to the best scores for each fold. l1_ratio_ is of shape(n_classes,) when the problem is binary.
Actual number of iterations for all classes, folds and Cs. In the binary or multinomial cases, the first dimension is equal to 1. If penalty='elasticnet', the shape is (n_classes, n_folds,
n_cs, n_l1_ratios) or (1, n_folds, n_cs, n_l1_ratios).
See also
decision_function(X)
Predict confidence scores for samples.
densify()
Convert coefficient matrix to dense array format.
fit(X, y[, sample_weight])
Fit the model according to the given training data.
get_params([deep])
Get parameters for this estimator.
predict(X)
Predict class labels for samples in X.
predict_log_proba(X)
Predict logarithm of probability estimates.
predict_proba(X)
Probability estimates.
score(X, y[, sample_weight])
Returns the score using the scoring option on the given test data and labels.
set_params(**params)
Set the parameters of this estimator.
sparsify()
Convert coefficient matrix to sparse format.
Predict confidence scores for samples.
The confidence score for a sample is proportional to the signed distance of that sample to the hyperplane.
Samples.
Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.
Convert coefficient matrix to dense array format.
Converts the coef_ member (back) to a numpy.ndarray. This is the default format of coef_ and is required for fitting, so calling this method is only required on models that have previously been sparsified; otherwise, it is a no-op.
Fitted estimator.
Fit the model according to the given training data.
Training vector, where n_samples is the number of samples and n_features is the number of features.
Target vector relative to X.
Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Predict class labels for samples in X.
Samples.
Predicted class label per sample.
Predict logarithm of probability estimates.
The returned estimates for all classes are ordered by the label of classes.
Vector to be scored, where n_samples is the number of samples and n_features is the number of features.
Returns the log-probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.
Probability estimates.
The returned estimates for all classes are ordered by the label of classes.
For a multi_class problem, if multi_class is set to be “multinomial” the softmax function is used to find the predicted probability of each class. Else use a one-vs-rest approach, i.e calculate the probability of each class assuming it to be positive using the logistic function. and normalize these values across all the classes.
Vector to be scored, where n_samples is the number of samples and n_features is the number of features.
Returns the probability of the sample for each class in the model, where classes are ordered as they are in self.classes_.
Returns the score using the scoring option on the given test data and labels.
Test samples.
True labels for X.
Sample weights.
Score of self.predict(X) wrt. y.
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.
Convert coefficient matrix to sparse format.
Converts the coef_ member to a scipy.sparse matrix, which for L1-regularized models can be much more memory- and storage-efficient than the usual numpy.ndarray representation.
The intercept_ member is not converted.
Fitted estimator.
For non-sparse models, i.e. when there are not many zeros in coef_, this may actually increase memory usage, so use this method with care. A rule of thumb is that the number of zero elements, which can be computed with (coef_ == 0).sum(), must be more than 50% for this to provide significant benefits.
After calling this method, further fitting with the partial_fit method (if any) will not work until you call densify.


Fit the model according to the given training data.
Training vector, where n_samples is the number of samples and n_features is the number of features.
Target vector relative to X.
Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight.


Returns the score using the scoring option on the given test data and labels.
Test samples.
True labels for X.
Sample weights.
Score of self.predict(X) wrt. y.


Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer.
The optimization objective for MultiTaskElasticNet is:
Where:
i.e. the sum of norms of each row.
Read more in the User Guide.
Constant that multiplies the L1/L2 term. Defaults to 1.0.
The ElasticNet mixing parameter, with 0 < l1_ratio <= 1. For l1_ratio = 1 the penalty is an L1/L2 penalty. For l1_ratio = 0 it is an L2 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1/L2 and L2.
Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
If True, X will be copied; else, it may be overwritten.
The maximum number of iterations.
The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.
The seed of the pseudo random number generator that selects a random feature to update. Used when selection == ‘random’. Pass an int for reproducible output across multiple function calls. See Glossary.
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.
Independent term in decision function.
Parameter vector (W in the cost function formula). If a 1D y is passed in at fit (non multi-task usage), coef_ is then a 1D array. Note that coef_ stores the transpose of W, W.T.
Number of iterations run by the coordinate descent solver to reach the specified tolerance.
The dual gaps at the end of the optimization.
The tolerance scaled scaled by the variance of the target y.
Sparse representation of the fitted coef_.
See also
Multi-task L1/L2 ElasticNet with built-in cross-validation.
The algorithm used to fit the model is coordinate descent.
To avoid unnecessary memory duplication the X and y arguments of the fit method should be directly passed as Fortran-contiguous numpy arrays.
fit(X, y)
Fit MultiTaskElasticNet model with coordinate descent
get_params([deep])
Get parameters for this estimator.
path(*args, **kwargs)
Compute elastic net path with coordinate descent.
predict(X)
Predict using the linear model.
score(X, y[, sample_weight])
Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params)
Set the parameters of this estimator.
Fit MultiTaskElasticNet model with coordinate descent
Data.
Target. Will be cast to X’s dtype if necessary.
Coordinate descent is an algorithm that considers each column of data at a time hence it will automatically convert the X input as a Fortran-contiguous numpy array if necessary.
To avoid memory re-allocation it is advised to allocate the initial data in memory directly using that format.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Compute elastic net path with coordinate descent.
The elastic net optimization function varies for mono and multi-outputs.
For mono-output tasks it is:
For multi-output tasks it is:
Where:
i.e. the sum of norm of each row.
Read more in the User Guide.
Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output then X can be sparse.
Target values.
Number between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). l1_ratio=1 corresponds to the Lasso.
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.
Number of alphas along the regularization path.
List of alphas where to compute the models. If None alphas are set automatically.
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
If True, X will be copied; else, it may be overwritten.
The initial values of the coefficients.
Amount of verbosity.
Whether to return the number of iterations or not.
If set to True, forces coefficients to be positive. (Only allowed when y.ndim == 1).
If set to False, the input validation checks are skipped (including the Gram matrix when provided). It is assumed that they are handled by the caller.
Keyword arguments passed to the coordinate descent solver.
The alphas along the path where models are computed.
Coefficients along the path.
The dual gaps at the end of the optimization for each alpha.
The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha. (Is returned when return_n_iter is set to True).
See also
For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.
Predict using the linear model.
Samples.
Returns predicted values.
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Estimator parameters.
Estimator instance.
Sparse representation of the fitted coef_.


Fit MultiTaskElasticNet model with coordinate descent
Data.
Target. Will be cast to X’s dtype if necessary.
Coordinate descent is an algorithm that considers each column of data at a time hence it will automatically convert the X input as a Fortran-contiguous numpy array if necessary.
To avoid memory re-allocation it is advised to allocate the initial data in memory directly using that format.


Compute elastic net path with coordinate descent.
The elastic net optimization function varies for mono and multi-outputs.
For mono-output tasks it is:
For multi-output tasks it is:
Where:
i.e. the sum of norm of each row.
Read more in the User Guide.
Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output then X can be sparse.
Target values.
Number between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). l1_ratio=1 corresponds to the Lasso.
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.
Number of alphas along the regularization path.
List of alphas where to compute the models. If None alphas are set automatically.
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
If True, X will be copied; else, it may be overwritten.
The initial values of the coefficients.
Amount of verbosity.
Whether to return the number of iterations or not.
If set to True, forces coefficients to be positive. (Only allowed when y.ndim == 1).
If set to False, the input validation checks are skipped (including the Gram matrix when provided). It is assumed that they are handled by the caller.
Keyword arguments passed to the coordinate descent solver.
The alphas along the path where models are computed.
Coefficients along the path.
The dual gaps at the end of the optimization for each alpha.
The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha. (Is returned when return_n_iter is set to True).
See also
For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.


Predict using the linear model.
Samples.
Returns predicted values.


Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)
** 2).sum() and \(v\) is the total sum of squares ((y_true -
y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
True values for X.
Sample weights.
\(R^2\) of self.predict(X) wrt. y.
The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).


Sparse representation of the fitted coef_.