ElasticNetCV (original) (raw)
class sklearn.linear_model.ElasticNetCV(*, l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, 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 cross-validation 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 = 0the 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].
epsfloat, default=1e-3
Length of the path. eps=1e-3 means thatalpha_min / alpha_max = 1e-3.
n_alphasint, default=100
Number of alphas along the regularization path, used for each l1_ratio.
alphasarray-like, 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).
precompute‘auto’, bool or array-like 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=1e-4
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.
cvint, cross-validation generator or iterable, default=None
Determines the cross-validation splitting strategy. Possible inputs for cv are:
- None, to use the default 5-fold cross-validation,
- int, to specify the number of folds.
- CV splitter,
- An iterable yielding (train, test) splits as arrays of indices.
For int/None inputs, KFold is used.
Refer User Guide for the various cross-validation strategies that can be used here.
Changed in version 0.22: cv default value if None changed from 3-fold to 5-fold.
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 a joblib.parallel_backend context.-1 means using all processors. See Glossaryfor 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 1e-4.
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.
**dual_gap_**float
The dual gaps at the end of the optimization for the optimal alpha.
**n_iter_**int
Number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.
**n_features_in_**int
Number of features seen during fit.
Added in version 0.24.
**feature_names_in_**ndarray of shape (n_features_in_,)
Names of features seen during fit. Defined only when Xhas feature names that are all strings.
Added in version 1.0.
See also
Compute elastic net path with coordinate descent.
Linear regression with combined L1 and L2 priors as regularizer.
Notes
In fit, once the best parameters l1_ratio and alpha are found through cross-validation, the model is fit again using the entire training set.
To avoid unnecessary memory duplication the X argument of the fitmethod 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:
for:
alpha = a + b and l1_ratio = a / (a + b).
For an example, seeexamples/linear_model/plot_lasso_model_selection.py.
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...]
fit(X, y, sample_weight=None, **params)[source]#
Fit ElasticNet model with coordinate descent.
Fit is on grid of alphas and best alpha estimated by cross-validation.
Parameters:
X{array-like, sparse matrix} of shape (n_samples, n_features)
Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output, X can be sparse. Note that large sparse matrices and arrays requiring int64 indices are not accepted.
yarray-like of shape (n_samples,)
Target values.
sample_weightfloat or array-like of shape (n_samples,), default=None
Sample weights used for fitting and evaluation of the weighted mean squared error of each cv-fold. Note that the cross validated MSE that is finally used to find the best model is the unweighted mean over the (weighted) MSEs of each test fold.
**paramsdict, default=None
Parameters to be passed to the CV splitter.
Added in version 1.4: Only available if enable_metadata_routing=True, which can be set by usingsklearn.set_config(enable_metadata_routing=True). See Metadata Routing User Guide for more details.
Returns:
selfobject
Returns an instance of fitted model.
get_metadata_routing()[source]#
Get metadata routing of this object.
Please check User Guide on how the routing mechanism works.
Added in version 1.4.
Returns:
routingMetadataRouter
A MetadataRouter encapsulating routing information.
get_params(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:
paramsdict
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, sparse matrix} of shape (n_samples, n_features)
Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output then Xcan be sparse.
y{array-like, sparse matrix} of shape (n_samples,) or (n_samples, n_targets)
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=1e-3
Length of the path. eps=1e-3 means thatalpha_min / alpha_max = 1e-3.
n_alphasint, default=100
Number of alphas along the regularization path.
alphasarray-like, default=None
List of alphas where to compute the models. If None alphas are set automatically.
precompute‘auto’, bool or array-like 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.
Xyarray-like of shape (n_features,) or (n_features, n_targets), 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_initarray-like 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
If set to False, the input validation checks are skipped (including the Gram matrix when provided). It is assumed that they are handled by the caller.
**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_targets, 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).
See also
Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer.
Multi-task L1/L2 ElasticNet with built-in cross-validation.
Linear regression with combined L1 and L2 priors as regularizer.
Elastic Net model with iterative fitting along a regularization path.
Notes
For an example, seeexamples/linear_model/plot_lasso_lasso_lars_elasticnet_path.py.
Examples
from sklearn.linear_model import enet_path from sklearn.datasets import make_regression X, y, true_coef = make_regression( ... n_samples=100, n_features=5, n_informative=2, coef=True, random_state=0 ... ) true_coef array([ 0. , 0. , 0. , 97.9..., 45.7...]) alphas, estimated_coef, _ = enet_path(X, y, n_alphas=3) alphas.shape (3,) estimated_coef array([[ 0. , 0.78..., 0.56...], [ 0. , 1.12..., 0.61...], [-0. , -2.12..., -1.12...], [ 0. , 23.04..., 88.93...], [ 0. , 10.63..., 41.56...]])
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(X, y, sample_weight=None)[source]#
Return the coefficient of determination of the prediction.
The coefficient of determination \(R^2\) is defined as\((1 - \frac{u}{v})\), 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:
Xarray-like 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 with shape(n_samples, n_samples_fitted), where n_samples_fittedis the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)
True values for X.
sample_weightarray-like of shape (n_samples,), default=None
Sample weights.
Returns:
scorefloat
\(R^2\) of self.predict(X) w.r.t. y.
Notes
The \(R^2\) score used when calling score on a regressor usesmultioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except forMultiOutputRegressor).
set_fit_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → ElasticNetCV[source]#
Request metadata passed to the fit method.
Note that this method is only relevant ifenable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.
The options for each parameter are:
True: metadata is requested, and passed tofitif provided. The request is ignored if metadata is not provided.False: metadata is not requested and the meta-estimator will not pass it tofit.None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.str: metadata should be passed to the meta-estimator with this given alias instead of the original name.
The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.
Added in version 1.3.
Note
This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside aPipeline. Otherwise it has no effect.
Parameters:
sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED
Metadata routing for sample_weight parameter in fit.
Returns:
selfobject
The updated object.
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as Pipeline). 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:
selfestimator instance
Estimator instance.
set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → ElasticNetCV[source]#
Request metadata passed to the score method.
Note that this method is only relevant ifenable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.
The options for each parameter are:
True: metadata is requested, and passed toscoreif provided. The request is ignored if metadata is not provided.False: metadata is not requested and the meta-estimator will not pass it toscore.None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.str: metadata should be passed to the meta-estimator with this given alias instead of the original name.
The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.
Added in version 1.3.
Note
This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside aPipeline. Otherwise it has no effect.
Parameters:
sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED
Metadata routing for sample_weight parameter in score.
Returns:
selfobject
The updated object.