3.2.4.1.1. `sklearn.linear_model`.ElasticNetCV¶

class sklearn.linear_model.ElasticNetCV(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]¶

Elastic Net model with iterative fitting along a regularization path

The best model is selected by cross-validation.

Read more in the User Guide.

Parameters:

l1_ratio : float, optional

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]

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, used for each l1_ratio.

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 cross-validation generator, optional

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

verbose : bool or integer

Amount of verbosity.

n_jobs : integer, optional

Number of CPUs to use during the cross validation. If -1, use all the CPUs.

positive : bool, optional

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

selection : str, 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.

random_state : int, RandomState instance, or None (default)

The seed of the pseudo random number generator that selects a random feature to update. Useful only when selection is set to ‘random’.

fit_intercept : boolean

whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).

normalize : boolean, optional, default False

If True, the regressors X will be normalized before regression.

copy_X : boolean, optional, default True

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

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_ : array, shape (n_features,) | (n_targets, n_features)

Parameter vector (w in the cost function formula),

intercept_ : float | array, shape (n_targets, n_features)

Independent term in the decision function.

mse_path_ : array, shape (n_l1_ratio, n_alpha, n_folds)

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

alphas_ : numpy array, shape (n_alphas,) or (n_l1_ratio, n_alphas)

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

n_iter_ : int

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

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 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

`decision_function`(args, *kwargs)	DEPRECATED: and will be removed in 0.19.
`fit`(X, y)	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`(X)	Predict using the linear model
`score`(X, y[, sample_weight])	Returns the coefficient of determination R^2 of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

__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, **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.

3.2.4.1.1. sklearn.linear_model.ElasticNetCV¶

3.2.4.1.1. `sklearn.linear_model`.ElasticNetCV¶