ElasticNet #

classsklearn.linear_model.ElasticNet(alpha=1.0,*,l1_ratio=0.5,fit_intercept=True,precompute=False,max_iter=1000,copy_X=True,tol=0.0001,warm_start=False,positive=False,random_state=None,selection='cyclic')[source]#

Linear regression with combined L1 and L2 priors as regularizer.

Minimizes the objective function:

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 penaltyseparately, keep in mind that this is equivalent to:

a*||w||_1+0.5*b*||w||_2^2

where:

alpha=a+bandl1_ratio=a/(a+b)

The parameter l1_ratio corresponds to alpha in the glmnet R package whilealpha corresponds to the lambda parameter in glmnet. Specifically, l1_ratio= 1 is the lasso penalty. Currently, l1_ratio <= 0.01 is not reliable,unless you supply your own sequence of alpha.

See also

ElasticNetCV: Elastic net model with best model selection by cross-validation.
SGDRegressor: Implements elastic net regression with incremental training.
SGDClassifier: Implements logistic regression with elastic net penalty (SGDClassifier(loss="log_loss",penalty="elasticnet")).

Notes

To avoid unnecessary memory duplication the X argument of the fit methodshould be directly passed as a Fortran-contiguous numpy array.

The precise stopping criteria based ontol are the following: First, check thatthat maximum coordinate update, i.e.$\max_j |w_j^{new} - w_j^{old}|$is smaller thantol times the maximum absolute coefficient,$\max_j |w_j|$.If so, then additionally check whether the dual gap is smaller thantol times$||y||_2^2 / n_{ ext{samples}}$.

Examples

>>>fromsklearn.linear_modelimportElasticNet>>>fromsklearn.datasetsimportmake_regression

>>>X,y=make_regression(n_features=2,random_state=0)>>>regr=ElasticNet(random_state=0)>>>regr.fit(X,y)ElasticNet(random_state=0)>>>print(regr.coef_)[18.83816048 64.55968825]>>>print(regr.intercept_)1.451>>>print(regr.predict([[0,0]]))[1.451]

L1-based models for Sparse Signalsshowcases ElasticNet alongside Lasso and ARD Regression for sparsesignal recovery in the presence of noise and feature correlation.

fit(X,y,sample_weight=None,check_input=True)[source]#

Fit model with coordinate descent.

Parameters:

X{ndarray, sparse matrix, sparse array} of (n_samples, n_features)

Data.

Note that large sparse matrices and arrays requiringint64indices are not accepted.

yndarray of shape (n_samples,) or (n_samples, n_targets)

Target. Will be cast to X’s dtype if necessary.

sample_weightfloat or array-like of shape (n_samples,), default=None

Sample weights. Internally, thesample_weight vector will berescaled to sum ton_samples.

Added in version 0.23.

check_inputbool, default=True

Allow to bypass several input checking.Don’t use this parameter unless you know what you do.

Returns:

selfobject: Fitted estimator.

Notes

Coordinate descent is an algorithm that considers each column ofdata at a time hence it will automatically convert the X inputas a Fortran-contiguous numpy array if necessary.

To avoid memory re-allocation it is advised to allocate theinitial data in memory directly using that format.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please checkUser Guide on how the routingmechanism works.

Returns:

routingMetadataRequest: AMetadataRequest encapsulatingrouting information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator andcontained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

staticpath(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_jw_{ij}^2}

i.e. the sum of norm of each row.

See also

MultiTaskElasticNet: Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer.
MultiTaskElasticNetCV: Multi-task L1/L2 ElasticNet with built-in cross-validation.
ElasticNet: Linear regression with combined L1 and L2 priors as regularizer.
ElasticNetCV: 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

>>>fromsklearn.linear_modelimportenet_path>>>fromsklearn.datasetsimportmake_regression>>>X,y,true_coef=make_regression(...n_samples=100,n_features=5,n_informative=2,coef=True,random_state=0...)>>>true_coefarray([ 0.        ,  0.        ,  0.        , 97.9, 45.7])>>>alphas,estimated_coef,_=enet_path(X,y,n_alphas=3)>>>alphas.shape(3,)>>>estimated_coef array([[ 0.,  0.787,  0.568],        [ 0.,  1.120,  0.620],        [-0., -2.129, -1.128],        [ 0., 23.046, 88.939],        [ 0., 10.637, 41.566]])

predict(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(X,y,sample_weight=None)[source]#

Returncoefficient of determination on test data.

The coefficient of determination,$R^2$, is defined as$(1 - \frac{u}{v})$, where$u$ is the residualsum 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 themodel can be arbitrarily worse). A constant model that always predictsthe expected value ofy, disregarding the input features, would geta$R^2$ score of 0.0.

Parameters:

Xarray-like of shape (n_samples, n_features): Test samples. For some estimators this may be a precomputedkernel matrix or a list of generic objects instead with shape(n_samples,n_samples_fitted), wheren_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 forX.
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.

Returns:

scorefloat: $R^2$ ofself.predict(X) w.r.t.y.

Notes

The$R^2$ score used when callingscore on a regressor usesmultioutput='uniform_average' from version 0.23 to keep consistentwith default value ofr2_score.This influences thescore method of all the multioutputregressors (except forMultiOutputRegressor).

set_fit_request(*,sample_weight:bool|None|str='$UNCHANGED$')→ElasticNet[source]#

Configure whether metadata should be requested to be passed to thefit method.

Note that this method is only relevant when this estimator is used as asub-estimator within ameta-estimator and metadata routing is enabledwithenable_metadata_routing=True (seesklearn.set_config).Please check theUser Guide on how the routingmechanism works.

The options for each parameter are:

True: metadata is requested, and passed tofit if 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 theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing forsample_weight parameter infit.

Returns:

selfobject: The updated object.

set_params(**params)[source]#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects(such asPipeline). The latter haveparameters of the form<component>__<parameter> so that it’spossible 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='$UNCHANGED$')→ElasticNet[source]#

Configure whether metadata should be requested to be passed to thescore method.

The options for each parameter are:

True: metadata is requested, and passed toscore if 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 theexisting request. This allows you to change the request for someparameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing forsample_weight parameter inscore.

Returns: