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=None, positive=False, random_state=None, selection='cyclic')[source]¶ Elastic Net model with iterative fitting along a regularization path.
See glossary entry for crossvalidation estimator.
Read more in the User Guide.
 Parameters
 l1_ratiofloat or list of float, default=0.5
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]
 epsfloat, default=1e3
Length of the path.
eps=1e3
means thatalpha_min / alpha_max = 1e3
. n_alphasint, default=100
Number of alphas along the regularization path, used for each l1_ratio.
 alphasndarray, default=None
List of alphas where to compute the models. If None alphas are set automatically
 fit_interceptbool, default=True
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
 normalizebool, default=False
This parameter is ignored when
fit_intercept
is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2norm. If you wish to standardize, please usesklearn.preprocessing.StandardScaler
before callingfit
on an estimator withnormalize=False
. precompute‘auto’, bool or arraylike of shape (n_features, n_features), default=’auto’
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_iterint, default=1000
The maximum number of iterations
 tolfloat, default=1e4
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
. cvint, crossvalidation generator or iterable, default=None
Determines the crossvalidation splitting strategy. Possible inputs for cv are:
None, to use the default 5fold crossvalidation,
int, to specify the number of folds.
An iterable yielding (train, test) splits as arrays of indices.
For int/None inputs,
KFold
is used.Refer User Guide for the various crossvalidation strategies that can be used here.
Changed in version 0.22:
cv
default value if None changed from 3fold to 5fold. copy_Xbool, default=True
If
True
, X will be copied; else, it may be overwritten. verbosebool or int, default=0
Amount of verbosity.
 n_jobsint, default=None
Number of CPUs to use during the cross validation.
None
means 1 unless in ajoblib.parallel_backend
context.1
means using all processors. See Glossary for more details. positivebool, default=False
When set to
True
, forces the coefficients to be positive. random_stateint, RandomState instance, default=None
The seed of the pseudo random number generator that selects a random feature to update. Used when
selection
== ‘random’. Pass an int for reproducible output across multiple function calls. See Glossary. selection{‘cyclic’, ‘random’}, 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.
 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_ndarray of shape (n_features,) or (n_targets, n_features)
Parameter vector (w in the cost function formula),
 intercept_float or ndarray of shape (n_targets, n_features)
Independent term in the decision function.
 mse_path_ndarray of shape (n_l1_ratio, n_alpha, n_folds)
Mean square error for the test set on each fold, varying l1_ratio and alpha.
 alphas_ndarray of 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
Notes
For an example, see examples/linear_model/plot_lasso_model_selection.py.
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).
Examples
>>> from sklearn.linear_model import ElasticNetCV >>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=2, random_state=0) >>> regr = ElasticNetCV(cv=5, random_state=0) >>> regr.fit(X, y) ElasticNetCV(cv=5, random_state=0) >>> print(regr.alpha_) 0.199... >>> print(regr.intercept_) 0.398... >>> print(regr.predict([[0, 0]])) [0.398...]
Methods
fit
(self, X, y)Fit linear 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])Return the coefficient of determination R^2 of the prediction.
set_params
(self, \*\*params)Set the parameters of this estimator.

__init__
(self, 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=None, positive=False, random_state=None, selection='cyclic')[source]¶ Initialize self. See help(type(self)) for accurate signature.

fit
(self, X, y)[source]¶ Fit linear model with coordinate descent
Fit is on grid of alphas and best alpha estimated by crossvalidation.
 Parameters
 X{arraylike, sparse matrix} of 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.
 yarraylike of shape (n_samples,) or (n_samples, n_targets)
Target values

get_params
(self, deep=True)[source]¶ Get parameters for this estimator.
 Parameters
 deepbool, default=True
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 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, sparse matrix} of 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{arraylike, sparse matrix} of shape (n_samples,) or (n_samples, n_outputs)
Target values.
 l1_ratiofloat, default=0.5
Number between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties).
l1_ratio=1
corresponds to the Lasso. epsfloat, default=1e3
Length of the path.
eps=1e3
means thatalpha_min / alpha_max = 1e3
. n_alphasint, default=100
Number of alphas along the regularization path.
 alphasndarray, default=None
List of alphas where to compute the models. If None alphas are set automatically.
 precompute‘auto’, bool or arraylike of shape (n_features, n_features), default=’auto’
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. Xyarraylike of shape (n_features,) or (n_features, n_outputs), default=None
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
 copy_Xbool, default=True
If
True
, X will be copied; else, it may be overwritten. coef_initndarray of shape (n_features, ), default=None
The initial values of the coefficients.
 verbosebool or int, default=False
Amount of verbosity.
 return_n_iterbool, default=False
Whether to return the number of iterations or not.
 positivebool, default=False
If set to True, forces coefficients to be positive. (Only allowed when
y.ndim == 1
). check_inputbool, default=True
Skip input validation checks, including the Gram matrix when provided assuming there are handled by the caller when check_input=False.
 **paramskwargs
Keyword arguments passed to the coordinate descent solver.
 Returns
 alphasndarray of shape (n_alphas,)
The alphas along the path where models are computed.
 coefsndarray of shape (n_features, n_alphas) or (n_outputs, n_features, n_alphas)
Coefficients along the path.
 dual_gapsndarray of shape (n_alphas,)
The dual gaps at the end of the optimization for each alpha.
 n_iterslist of int
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
For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.

predict
(self, X)[source]¶ Predict using the linear model.
 Parameters
 Xarray_like or sparse matrix, shape (n_samples, n_features)
Samples.
 Returns
 Carray, shape (n_samples,)
Returns predicted values.

score
(self, X, y, sample_weight=None)[source]¶ Return the coefficient of determination R^2 of the prediction.
The coefficient R^2 is defined as (1  u/v), where u is the residual sum of squares ((y_true  y_pred) ** 2).sum() and v is the total sum of squares ((y_true  y_true.mean()) ** 2).sum(). The 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
 Xarraylike of shape (n_samples, n_features)
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead, shape = (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
 yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for X.
 sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
R^2 of self.predict(X) wrt. y.
Notes
The R2 score used when calling
score
on a regressor usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).

set_params
(self, **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. Parameters
 **paramsdict
Estimator parameters.
 Returns
 selfobject
Estimator instance.