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8.14.1.7. sklearn.linear_model.ElasticNetCV

class sklearn.linear_model.ElasticNetCV(rho=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)

Elastic Net model with iterative fitting along a regularization path

The best model is selected by cross-validation.

Parameters :

rho : float, optional

float between 0 and 1 passed to ElasticNet (scaling between l1 and l2 penalties). For rho = 0 the penalty is an L1 penalty. For rho = 1 it is an L2 penalty. For 0 < rho < 1, the penalty is a combination of L1 and L2

eps : float, optional

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 : numpy array, 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.

max_iter: int, optional :

The maximum number of iterations

tol: float, optional :

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.

cv : integer or crossvalidation generator, optional

If an integer is passed, it is the number of fold (default 3). Specific crossvalidation objects can be passed, see sklearn.cross_validation module for the list of possible objects

verbose : bool or integer

amount of verbosity

See also

enet_path, ElasticNet

Notes

See examples/linear_model/lasso_path_with_crossvalidation.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 rho 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 * rho * ||w||_1 + 0.5 * alpha * (1 - rho) * ||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 rho = a / (a + b)

Methods

decision_function(X) Decision function of the linear model
estimator
fit(X, y) Fit linear model with coordinate descent along decreasing alphas
path(X, y[, rho, eps, n_alphas, alphas, ...]) Compute Elastic-Net path with coordinate descent
predict(X) Predict using the linear model
score(X, y) Returns the coefficient of determination R^2 of the prediction.
set_params(**params) Set the parameters of the estimator.
__init__(rho=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)
decision_function(X)

Decision function of the linear model

Parameters :

X : numpy array of shape [n_samples, n_features]

Returns :

C : array, shape = [n_samples]

Returns predicted values.

estimator

alias of ElasticNet

fit(X, y)

Fit linear model with coordinate descent along decreasing alphas using cross-validation

Parameters :

X : numpy array of shape [n_samples,n_features]

Training data. Pass directly as fortran contiguous data to avoid unnecessary memory duplication

y : numpy array of shape [n_samples]

Target values

fit_params : kwargs

keyword arguments passed to the Lasso fit method

static path(X, y, rho=0.5, eps=0.001, n_alphas=100, alphas=None, precompute='auto', Xy=None, fit_intercept=True, normalize=False, copy_X=True, verbose=False, **params)

Compute Elastic-Net path with coordinate descent

The Elastic Net optimization function is:

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

X : numpy array of shape [n_samples, n_features]

Training data. Pass directly as fortran contiguous data to avoid unnecessary memory duplication

y : numpy array of shape [n_samples]

Target values

rho : float, optional

float between 0 and 1 passed to ElasticNet (scaling between l1 and l2 penalties). rho=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 : numpy array, 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.

fit_intercept : bool

Fit or not an intercept

normalize : boolean, optional

If True, the regressors X are normalized

copy_X : boolean, optional, default True

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

verbose : bool or integer

Amount of verbosity

params : kwargs

keyword arguments passed to the Lasso objects

Returns :

models : a list of models along the regularization path

Notes

See examples/plot_lasso_coordinate_descent_path.py for an example.

predict(X)

Predict using the linear model

Parameters :

X : numpy array of shape [n_samples, n_features]

Returns :

C : array, shape = [n_samples]

Returns predicted values.

score(X, y)

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 - 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, lower values are worse.

Parameters :

X : array-like, shape = [n_samples, n_features]

Training set.

y : array-like, shape = [n_samples]

Returns :

z : float

set_params(**params)

Set the parameters of the estimator.

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

Returns :self :