sklearn.linear_model.ElasticNetCV¶

class sklearn.linear_model.ElasticNetCV(*, l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, precompute='auto', max_iter=1000, tol=0.0001, cv=None, copy_X=True, verbose=0, n_jobs=None, positive=False, random_state=None, selection='cyclic')[source]

Elastic Net model with iterative fitting along a regularization path.

See glossary entry for cross-validation estimator.

Read more in the User Guide.

Parameters:
l1_ratiofloat or list of float, default=0.5

Float between 0 and 1 passed to ElasticNet (scaling between l1 and l2 penalties). For l1_ratio = 0 the penalty is an L2 penalty. For l1_ratio = 1 it is an L1 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2 This parameter can be a list, in which case the different values are tested by cross-validation and the one giving the best prediction score is used. Note that a good choice of list of values for l1_ratio is often to put more values close to 1 (i.e. Lasso) and less close to 0 (i.e. Ridge), as in [.1, .5, .7, .9, .95, .99, 1].

epsfloat, default=1e-3

Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.

n_alphasint, default=100

Number of alphas along the regularization path, used for each l1_ratio.

alphasarray-like, default=None

List of alphas where to compute the models. If None alphas are set automatically.

fit_interceptbool, default=True

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).

precompute‘auto’, bool or array-like of shape (n_features, n_features), default=’auto’

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.

max_iterint, default=1000

The maximum number of iterations.

tolfloat, default=1e-4

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.

cvint, cross-validation generator or iterable, default=None

Determines the cross-validation splitting strategy. Possible inputs for cv are:

• None, to use the default 5-fold cross-validation,

• int, to specify the number of folds.

• An iterable yielding (train, test) splits as arrays of indices.

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.

copy_Xbool, default=True

If True, X will be copied; else, it may be overwritten.

verbosebool or int, default=0

Amount of verbosity.

n_jobsint, default=None

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.

positivebool, default=False

When set to True, forces the coefficients to be positive.

random_stateint, RandomState instance, default=None

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.

selection{‘cyclic’, ‘random’}, default=’cyclic’

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.

Attributes:
alpha_float

The amount of penalization chosen by cross validation.

l1_ratio_float

The compromise between l1 and l2 penalization chosen by cross validation.

coef_ndarray of shape (n_features,) or (n_targets, n_features)

Parameter vector (w in the cost function formula).

intercept_float or ndarray of shape (n_targets, n_features)

Independent term in the decision function.

mse_path_ndarray of shape (n_l1_ratio, n_alpha, n_folds)

Mean square error for the test set on each fold, varying l1_ratio and alpha.

alphas_ndarray of shape (n_alphas,) or (n_l1_ratio, n_alphas)

The grid of alphas used for fitting, for each l1_ratio.

dual_gap_float

The dual gaps at the end of the optimization for the optimal alpha.

n_iter_int

Number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.

n_features_in_int

Number of features seen during fit.

New in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

New in version 1.0.

enet_path

Compute elastic net path with coordinate descent.

ElasticNet

Linear regression with combined L1 and L2 priors as regularizer.

Notes

In fit, once the best parameters l1_ratio and alpha are found through cross-validation, the model is fit again using the entire training set.

To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

The parameter l1_ratio corresponds to alpha in the glmnet R package while alpha corresponds to the lambda parameter in glmnet. More specifically, the optimization objective is:

1 / (2 * n_samples) * ||y - Xw||^2_2
+ alpha * l1_ratio * ||w||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2


If you are interested in controlling the L1 and L2 penalty separately, keep in mind that this is equivalent to:

a * L1 + b * L2


for:

alpha = a + b and l1_ratio = a / (a + b).


For an example, see examples/linear_model/plot_lasso_model_selection.py.

Examples

>>> from sklearn.linear_model import ElasticNetCV
>>> from sklearn.datasets import make_regression

>>> X, y = make_regression(n_features=2, random_state=0)
>>> regr = ElasticNetCV(cv=5, random_state=0)
>>> regr.fit(X, y)
ElasticNetCV(cv=5, random_state=0)
>>> print(regr.alpha_)
0.199...
>>> print(regr.intercept_)
0.398...
>>> print(regr.predict([[0, 0]]))
[0.398...]


Methods

 fit(X, y[, sample_weight]) Fit linear model with coordinate descent. get_params([deep]) Get parameters for this estimator. path(X, y, *[, l1_ratio, eps, n_alphas, ...]) Compute elastic net path with coordinate descent. Predict using the linear model. score(X, y[, sample_weight]) Return the coefficient of determination of the prediction. set_params(**params) Set the parameters of this estimator.
fit(X, y, sample_weight=None)[source]

Fit linear model with coordinate descent.

Fit is on grid of alphas and best alpha estimated by cross-validation.

Parameters:
X{array-like, sparse matrix} of shape (n_samples, n_features)

Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output, X can be sparse.

yarray-like of shape (n_samples,) or (n_samples, n_targets)

Target values.

sample_weightfloat or array-like of shape (n_samples,), default=None

Sample weights used for fitting and evaluation of the weighted mean squared error of each cv-fold. Note that the cross validated MSE that is finally used to find the best model is the unweighted mean over the (weighted) MSEs of each test fold.

Returns:
selfobject

Returns an instance of fitted model.

get_params(deep=True)[source]

Get parameters for this estimator.

Parameters:
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:
paramsdict

Parameter names mapped to their values.

static path(X, y, *, l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, precompute='auto', Xy=None, copy_X=True, coef_init=None, verbose=False, return_n_iter=False, positive=False, check_input=True, **params)[source]

Compute elastic net path with coordinate descent.

The elastic net optimization function varies for mono and multi-outputs.

For mono-output tasks it is:

1 / (2 * n_samples) * ||y - Xw||^2_2
+ alpha * l1_ratio * ||w||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2


For multi-output tasks it is:

(1 / (2 * n_samples)) * ||Y - XW||_Fro^2
+ alpha * l1_ratio * ||W||_21
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2


Where:

||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}


i.e. the sum of norm of each row.

Read more in the User Guide.

Parameters:
X{array-like, sparse matrix} of shape (n_samples, n_features)

Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output then X can be sparse.

y{array-like, sparse matrix} of shape (n_samples,) or (n_samples, n_targets)

Target values.

l1_ratiofloat, default=0.5

Number between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). l1_ratio=1 corresponds to the Lasso.

epsfloat, default=1e-3

Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.

n_alphasint, default=100

Number of alphas along the regularization path.

alphasndarray, default=None

List of alphas where to compute the models. If None alphas are set automatically.

precompute‘auto’, bool or array-like of shape (n_features, n_features), default=’auto’

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.

Xyarray-like of shape (n_features,) or (n_features, n_targets), default=None

Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.

copy_Xbool, default=True

If True, X will be copied; else, it may be overwritten.

coef_initndarray of shape (n_features, ), default=None

The initial values of the coefficients.

verbosebool or int, default=False

Amount of verbosity.

return_n_iterbool, default=False

Whether to return the number of iterations or not.

positivebool, default=False

If set to True, forces coefficients to be positive. (Only allowed when y.ndim == 1).

check_inputbool, default=True

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.

**paramskwargs

Keyword arguments passed to the coordinate descent solver.

Returns:
alphasndarray of shape (n_alphas,)

The alphas along the path where models are computed.

coefsndarray of shape (n_features, n_alphas) or (n_targets, n_features, n_alphas)

Coefficients along the path.

dual_gapsndarray of shape (n_alphas,)

The dual gaps at the end of the optimization for each alpha.

n_iterslist of int

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).

MultiTaskElasticNet

Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer.

MultiTaskElasticNetCV

Multi-task L1/L2 ElasticNet with built-in cross-validation.

ElasticNet

Linear regression with combined L1 and L2 priors as regularizer.

ElasticNetCV

Elastic Net model with iterative fitting along a regularization path.

Notes

For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.

predict(X)[source]

Predict using the linear model.

Parameters:
Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.

Returns:
Carray, shape (n_samples,)

Returns predicted values.

score(X, y, sample_weight=None)[source]

Return the coefficient of determination of the prediction.

The coefficient of determination $$R^2$$ 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.

Parameters:
Xarray-like of shape (n_samples, n_features)

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.

yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

Returns:
scorefloat

$$R^2$$ of self.predict(X) w.r.t. y.

Notes

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_params(**params)[source]

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.

Parameters:
**paramsdict

Estimator parameters.

Returns:
selfestimator instance

Estimator instance.