RidgeCV

classsklearn.linear_model.RidgeCV(alphas=(0.1, 1.0, 10.0), *, fit_intercept=True, scoring=None, cv=None, gcv_mode=None, store_cv_results=False, alpha_per_target=False)[source]

Ridge regression with built-in cross-validation.

See glossary entry for cross-validation estimator.

By default, it performs efficient Leave-One-Out Cross-Validation.

Read more in the User Guide.

Parameters:

alphasarray-like of shape (n_alphas,), default=(0.1, 1.0, 10.0)

Array of alpha values to try. Regularization strength; must be a positive float. Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to 1 / (2C) in other linear models such as LogisticRegression or LinearSVC. If using Leave-One-Out cross-validation, alphas must be strictly positive.

For an example on how regularization strength affects the model coefficients, see Ridge coefficients as a function of the L2 Regularization.

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).

scoringstr, callable, default=None

The scoring method to use for cross-validation. Options:

• str: see String name scorers for options.
• callable: a scorer callable object (e.g., function) with signature scorer(estimator, X, y). See Callable scorers for details.
• None: negative mean squared error if cv is None (i.e. when using leave-one-out cross-validation), or coefficient of determination (\(R^2\)) otherwise.

cvint, cross-validation generator or an iterable, default=None

Determines the cross-validation splitting strategy. Possible inputs for cv are:

• None, to use the efficient Leave-One-Out cross-validation
• integer, to specify the number of folds,
• CV splitter,
• an iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, if y is binary or multiclass, StratifiedKFold is used, else, KFold is used.

Refer User Guide for the various cross-validation strategies that can be used here.

gcv_mode{‘auto’, ‘svd’, ‘eigen’}, default=’auto’

Flag indicating which strategy to use when performing Leave-One-Out Cross-Validation. Options are:

'auto' : same as 'eigen'
'svd' : use singular value decomposition of X when X is dense,
    fallback to 'eigen' when X is sparse
'eigen' : use eigendecomposition of X X' when n_samples <= n_features
    or X' X when n_features < n_samples

The ‘auto’ mode is the default and is intended to pick the cheaper option depending on the shape and sparsity of the training data.

store_cv_resultsbool, default=False

Flag indicating if the cross-validation values corresponding to each alpha should be stored in the cv_results_ attribute (see below). This flag is only compatible with cv=None (i.e. using Leave-One-Out Cross-Validation).

Changed in version 1.5: Parameter name changed from store_cv_values to store_cv_results.

alpha_per_targetbool, default=False

Flag indicating whether to optimize the alpha value (picked from the alphas parameter list) for each target separately (for multi-output settings: multiple prediction targets). When set to True, after fitting, the alpha_ attribute will contain a value for each target. When set to False, a single alpha is used for all targets. This flag is only compatible with cv=None (i.e. using Leave-One-Out Cross-Validation).

Added in version 0.24.

Attributes:

cv_results_ndarray of shape (n_samples, n_alphas) or shape (n_samples, n_targets, n_alphas), optional

Cross-validation values for each alpha (only available if store_cv_results=True and cv=None). After fit() has been called, this attribute will contain the mean squared errors if scoring is None otherwise it will contain standardized per point prediction values.

Changed in version 1.5: cv_values_ changed to cv_results_.

coef_ndarray of shape (n_features) or (n_targets, n_features)

Weight vector(s).

intercept_float or ndarray of shape (n_targets,)

Independent term in decision function. Set to 0.0 if fit_intercept = False.

alpha_float or ndarray of shape (n_targets,)

Estimated regularization parameter, or, if alpha_per_target=True, the estimated regularization parameter for each target.

best_score_float or ndarray of shape (n_targets,)

Score of base estimator with best alpha, or, if alpha_per_target=True, a score for each target.

Added in version 0.23.

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 X has feature names that are all strings.

Added in version 1.0.

See also

Ridge

Ridge regression.

RidgeClassifier

Classifier based on ridge regression on {-1, 1} labels.

RidgeClassifierCV

Ridge classifier with built-in cross validation.

Examples

>>> from sklearn.datasets import load_diabetes
>>> from sklearn.linear_model import RidgeCV
>>> X, y = load_diabetes(return_X_y=True)
>>> clf = RidgeCV(alphas=[1e-3, 1e-2, 1e-1, 1]).fit(X, y)
>>> clf.score(X, y)
0.5166...

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

Fit Ridge regression model with cv.

Parameters:

Xndarray of shape (n_samples, n_features)

Training data. If using GCV, will be cast to float64 if necessary.

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

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

sample_weightfloat or ndarray of shape (n_samples,), default=None

Individual weights for each sample. If given a float, every sample will have the same weight.

**paramsdict, default=None

Parameters to be passed to the underlying scorer.

Added in version 1.5: Only available if enable_metadata_routing=True, which can be set by using sklearn.set_config(enable_metadata_routing=True). See Metadata Routing User Guide for more details.

Returns:

selfobject

Fitted estimator.

Notes

When sample_weight is provided, the selected hyperparameter may depend on whether we use leave-one-out cross-validation (cv=None) or another form of cross-validation, because only leave-one-out cross-validation takes the sample weights into account when computing the validation score.

get_metadata_routing()[source]

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Added in version 1.5.

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.

predict(X)[source]

Predict using the linear model.

Parameters:

Xarray-like or sparse matrix of shape (n_samples, n_features)

Samples.

Returns:

Cndarray of shape (n_samples,) or (n_samples, n_outputs)

Predicted values.

score(X, y, sample_weight=None)[source]

Return coefficient of determination on test data.

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_fitted is 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 uses multioutput='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 for MultiOutputRegressor).

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

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
• False: metadata is not requested and the meta-estimator will not pass it to fit.
• 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.

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_params(**params)[source]

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='$UNCHANGED$') → RidgeCV[source]

Configure whether metadata should be requested to be passed to the score method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
• False: metadata is not requested and the meta-estimator will not pass it to score.
• 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.

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.

Gallery examples

Time-related feature engineering

Effect of transforming the targets in regression model

Combine predictors using stacking

Model-based and sequential feature selection

Common pitfalls in the interpretation of coefficients of linear models

Face completion with a multi-output estimators