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 crossvalidation.
Read more in the User Guide.
Parameters: l1_ratio : float or array of floats, 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. Forl1_ratio = 1
it is an L1 penalty. For0 < 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 crossvalidation 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=1e3
means thatalpha_min / alpha_max = 1e3
.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’  arraylike
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 thantol
.cv : int, crossvalidation generator or an iterable, optional
Determines the crossvalidation splitting strategy. Possible inputs for cv are:
 None, to use the default 3fold crossvalidation,
 integer, to specify the number of folds.
 An object to be used as a crossvalidation generator.
 An iterable yielding train/test splits.
For integer/None inputs,
KFold
is used.Refer User Guide for the various crossvalidation strategies that can be used here.
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 1e4.
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. This parameter is ignored whenfit_intercept
is set toFalse
. When the regressors are normalized, note that this makes the hyperparameters learnt more robust and almost independent of the number of samples. The same property is not valid for standardized data. However, if you wish to standardize, please usepreprocessing.StandardScaler
before callingfit
on an estimator withnormalize=False
.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/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 Fortrancontiguous 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
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]¶

fit
(X, y)[source]¶ Fit linear model with coordinate descent
Fit is on grid of alphas and best alpha estimated by crossvalidation.
Parameters: X : {arraylike}, shape (n_samples, n_features)
Training data. Pass directly as Fortrancontiguous data to avoid unnecessary memory duplication. If y is monooutput, X can be sparse.
y : arraylike, 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 multioutputs.
For monooutput 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 multioutput 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 : {arraylike}, shape (n_samples, n_features)
Training data. Pass directly as Fortrancontiguous data to avoid unnecessary memory duplication. If
y
is monooutput thenX
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 Lassoeps : float
Length of the path.
eps=1e3
means thatalpha_min / alpha_max = 1e3
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’  arraylike
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 : arraylike, 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 : arraylike, 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).Notes
See examples/linear_model/plot_lasso_coordinate_descent_path.py for an example.

predict
(X)[source]¶ Predict using the linear model
Parameters: X : {arraylike, 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 : arraylike, shape = (n_samples, n_features)
Test samples.
y : arraylike, shape = (n_samples) or (n_samples, n_outputs)
True values for X.
sample_weight : arraylike, 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 :