LassoCV #

classsklearn.linear_model.LassoCV(*,eps=0.001,n_alphas='deprecated',alphas='warn',fit_intercept=True,precompute='auto',max_iter=1000,tol=0.0001,copy_X=True,cv=None,verbose=False,n_jobs=None,positive=False,random_state=None,selection='cyclic')[source]#

Lasso linear model with iterative fitting along a regularization path.

See glossary entry forcross-validation estimator.

The best model is selected by cross-validation.

The optimization objective for Lasso is:

(1/(2*n_samples))*||y-Xw||^2_2+alpha*||w||_1

See also

lars_path: Compute Least Angle Regression or Lasso path using LARS algorithm.
lasso_path: Compute Lasso path with coordinate descent.
Lasso: The Lasso is a linear model that estimates sparse coefficients.
LassoLars: Lasso model fit with Least Angle Regression a.k.a. Lars.
LassoCV: Lasso linear model with iterative fitting along a regularization path.
LassoLarsCV: Cross-validated Lasso using the LARS algorithm.

Notes

Infit, once the best parameteralpha is found throughcross-validation, the model is fit again using the entire training set.

To avoid unnecessary memory duplication theX argument of thefitmethod should be directly passed as a Fortran-contiguous numpy array.

For an example, seeexamples/linear_model/plot_lasso_model_selection.py.

LassoCV leads to different results than a hyperparametersearch usingGridSearchCV with aLasso model. InLassoCV, a model for a givenpenaltyalpha is warm started using the coefficients of theclosest model (trained at the previous iteration) on theregularization path. It tends to speed up the hyperparametersearch.

Examples

>>>fromsklearn.linear_modelimportLassoCV>>>fromsklearn.datasetsimportmake_regression>>>X,y=make_regression(noise=4,random_state=0)>>>reg=LassoCV(cv=5,random_state=0).fit(X,y)>>>reg.score(X,y)0.9993>>>reg.predict(X[:1,])array([-78.4951])

fit(X,y,sample_weight=None,**params)[source]#

Fit Lasso 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 datato avoid unnecessary memory duplication. If y is mono-output,X can be sparse. Note that large sparse matrices and arraysrequiringint64 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 weightedmean squared error of each cv-fold. Note that the cross validatedMSE that is finally used to find the best model is the unweightedmean 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 ifenable_metadata_routing=True,which can be set by usingsklearn.set_config(enable_metadata_routing=True).SeeMetadata Routing User Guide formore details.

Returns:

selfobject: Returns an instance of fitted model.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please checkUser Guide on how the routingmechanism works.

Added in version 1.4.

Returns:

routingMetadataRouter: AMetadataRouter 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,*,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 Lasso path with coordinate descent.

The Lasso optimization function varies for mono and multi-outputs.

For mono-output tasks it is:

(1/(2*n_samples))*||y-Xw||^2_2+alpha*||w||_1

For multi-output tasks it is:

(1/(2*n_samples))*||Y-XW||^2_Fro+alpha*||W||_21

Where:

||W||_21= \sum_i \sqrt{\sum_jw_{ij}^2}

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

See also

lars_path: Compute Least Angle Regression or Lasso path using LARS algorithm.
Lasso: The Lasso is a linear model that estimates sparse coefficients.
LassoLars: Lasso model fit with Least Angle Regression a.k.a. Lars.
LassoCV: Lasso linear model with iterative fitting along a regularization path.
LassoLarsCV: Cross-validated Lasso using the LARS algorithm.
sklearn.decomposition.sparse_encode: Estimator that can be used to transform signals into sparse linear combination of atoms from a fixed.

Notes

For an example, seeexamples/linear_model/plot_lasso_lasso_lars_elasticnet_path.py.

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

Note that in certain cases, the Lars solver may be significantlyfaster to implement this functionality. In particular, linearinterpolation can be used to retrieve model coefficients between thevalues output by lars_path

Examples

Comparing lasso_path and lars_path with interpolation:

>>>importnumpyasnp>>>fromsklearn.linear_modelimportlasso_path>>>X=np.array([[1,2,3.1],[2.3,5.4,4.3]]).T>>>y=np.array([1,2,3.1])>>># Use lasso_path to compute a coefficient path>>>_,coef_path,_=lasso_path(X,y,alphas=[5.,1.,.5])>>>print(coef_path)[[0.         0.         0.46874778] [0.2159048  0.4425765  0.23689075]]

>>># Now use lars_path and 1D linear interpolation to compute the>>># same path>>>fromsklearn.linear_modelimportlars_path>>>alphas,active,coef_path_lars=lars_path(X,y,method='lasso')>>>fromscipyimportinterpolate>>>coef_path_continuous=interpolate.interp1d(alphas[::-1],...coef_path_lars[:,::-1])>>>print(coef_path_continuous([5.,1.,.5]))[[0.         0.         0.46915237] [0.2159048  0.4425765  0.23668876]]

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='$UNCHANGED$')→LassoCV[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='$UNCHANGED$')→LassoCV[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: