`sklearn.linear_model`.ElasticNet¶

class sklearn.linear_model.ElasticNet(alpha=1.0, l1_ratio=0.5, fit_intercept=True, normalize=False, precompute=False, max_iter=1000, copy_X=True, tol=0.0001, warm_start=False, positive=False, random_state=None, selection='cyclic')[source]¶

Linear regression with combined L1 and L2 priors as regularizer.

Minimizes the objective function:

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

where:

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

The parameter l1_ratio corresponds to alpha in the glmnet R package while alpha corresponds to the lambda parameter in glmnet. Specifically, l1_ratio = 1 is the lasso penalty. Currently, l1_ratio <= 0.01 is not reliable, unless you supply your own sequence of alpha.

See also

ElasticNetCV: Elastic net model with best model selection by cross-validation.
SGDRegressor: implements elastic net regression with incremental training.
SGDClassifier: implements logistic regression with elastic net penalty (SGDClassifier(loss="log", penalty="elasticnet")).

Notes

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

Examples

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

>>> X, y = make_regression(n_features=2, random_state=0)
>>> regr = ElasticNet(random_state=0)
>>> regr.fit(X, y)
ElasticNet(random_state=0)
>>> print(regr.coef_)
[18.83816048 64.55968825]
>>> print(regr.intercept_)
1.451...
>>> print(regr.predict([[0, 0]]))
[1.451...]

Methods

`fit`(self, X, y[, check_input])	Fit model with coordinate descent.
`get_params`(self[, deep])	Get parameters for this estimator.
`path`(X, y[, l1_ratio, eps, n_alphas, …])	Compute elastic net path with coordinate descent
`predict`(self, X)	Predict using the linear model
`score`(self, X, y[, sample_weight])	Returns the coefficient of determination R^2 of the prediction.
`set_params`(self, \\params)	Set the parameters of this estimator.

__init__(self, alpha=1.0, l1_ratio=0.5, fit_intercept=True, normalize=False, precompute=False, max_iter=1000, copy_X=True, tol=0.0001, warm_start=False, positive=False, random_state=None, selection='cyclic')[source]¶: Initialize self. See help(type(self)) for accurate signature.

fit(self, X, y, check_input=True)[source]¶

Fit model with coordinate descent.

Parameters

Xndarray or scipy.sparse matrix, (n_samples, n_features): Data
yndarray, shape (n_samples,) or (n_samples, n_targets): Target. Will be cast to X’s dtype if necessary
check_inputboolean, (default=True): Allow to bypass several input checking. Don’t use this parameter unless you know what you do.

Notes

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_params(self, deep=True)[source]¶

Get parameters for this estimator.

Parameters

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

Returns

paramsmapping of string to any: 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.

sklearn.linear_model.ElasticNet¶

`sklearn.linear_model`.ElasticNet¶