linear_model.ElasticNetCV()

Elastic Net model with iterative fitting along a regularization path

The best model is selected by cross-validation.

Read more in the User Guide.

Notes

See examples/linear_model/plot_lasso_model_selection.py for an example.

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).

Methods

__init__(l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, precompute='auto', max_iter=1000, tol=0.0001, cv=None, copy_X=True, verbose=0, n_jobs=1, positive=False, random_state=None, selection='cyclic') [source]

decision_function(*args, **kwargs) [source]

DEPRECATED: and will be removed in 0.19.

Decision function of the linear model.

Parameters:	X : {array-like, sparse matrix}, shape = (n_samples, n_features) Samples.
Returns:	C : array, shape = (n_samples,) Returns predicted values.

fit(X, y) [source]

Fit linear model with coordinate descent

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

Parameters:	X : {array-like}, shape (n_samples, n_features) Training data. Pass directly as float64, Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output, X can be sparse. y : array-like, shape (n_samples,) or (n_samples, n_targets) Target values

get_params(deep=True) [source]

Get parameters for this estimator.

Parameters:	deep : boolean, optional If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:	params : mapping 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.

Read more in the User Guide.

Parameters:

X : {array-like}, 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 : ndarray, shape (n_samples,) or (n_samples, n_outputs) Target values l1_ratio : float, optional float between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). l1_ratio=1 corresponds to the Lasso eps : float Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3 n_alphas : int, optional Number of alphas along the regularization path alphas : ndarray, optional List of alphas where to compute the models. If None alphas are set automatically precompute : True | False | ?auto? | array-like 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 : array-like, optional Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed. copy_X : boolean, optional, default True If True, X will be copied; else, it may be overwritten. coef_init : array, shape (n_features, ) | None The initial values of the coefficients. verbose : bool or integer Amount of verbosity. params : kwargs keyword arguments passed to the coordinate descent solver. return_n_iter : bool whether to return the number of iterations or not. positive : bool, default False If set to True, forces coefficients to be positive. check_input : bool, default True Skip input validation checks, including the Gram matrix when provided assuming there are handled by the caller when check_input=False.

Returns:

alphas : array, shape (n_alphas,) The alphas along the path where models are computed. coefs : array, shape (n_features, n_alphas) or (n_outputs, n_features, n_alphas) Coefficients along the path. dual_gaps : array, shape (n_alphas,) The dual gaps at the end of the optimization for each alpha. n_iters : array-like, shape (n_alphas,) 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

MultiTaskElasticNet, MultiTaskElasticNetCV, ElasticNet, ElasticNetCV

Notes

See examples/linear_model/plot_lasso_coordinate_descent_path.py for an example.

predict(X) [source]

Predict using the linear model

Parameters:	X : {array-like, sparse matrix}, shape = (n_samples, n_features) Samples.
Returns:	C : array, shape = (n_samples,) Returns predicted values.

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

Returns the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - u/v), where u is the regression sum of squares ((y_true - y_pred) ** 2).sum() and v is the residual sum of squares ((y_true - y_true.mean()) ** 2).sum(). 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:	X : array-like, shape = (n_samples, n_features) Test samples. y : array-like, shape = (n_samples) or (n_samples, n_outputs) True values for X. sample_weight : array-like, shape = [n_samples], optional Sample weights.
Returns:	score : float R^2 of self.predict(X) wrt. y.

set_params(**params) [source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it?s possible to update each component of a nested object.

Returns:	self :