class sklearn.linear_model.RidgeCV(alphas=0.1, 1.0, 10.0, *, fit_intercept=True, normalize=False, scoring=None, cv=None, gcv_mode=None, store_cv_values=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.

alphasndarray 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 positive.

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 l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.

scoringstring, callable, default=None

A string (see model evaluation documentation) or a scorer callable object / function with signature scorer(estimator, X, y). If None, the negative mean squared error if cv is ‘auto’ or None (i.e. when using leave-one-out cross-validation), and r2 score 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' : use 'svd' if n_samples > n_features, otherwise use 'eigen'
'svd' : force use of singular value decomposition of X when X is
    dense, eigenvalue decomposition of X^T.X when X is sparse.
'eigen' : force computation via eigendecomposition of X.X^T

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

store_cv_valuesbool, default=False

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

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.

New in version 0.24.

cv_values_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_values=True and cv=None). After fit() has been called, this attribute will contain the mean squared errors (by default) or the values of the {loss,score}_func function (if provided in the constructor).

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.

New in version 0.23.

See also


Ridge regression.


Ridge classifier.


Ridge classifier with built-in cross validation.


>>> 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)


fit(X, y[, sample_weight])

Fit Ridge regression model with cv.


Get parameters for this estimator.


Predict using the linear model.

score(X, y[, sample_weight])

Return the coefficient of determination \(R^2\) of the prediction.


Set the parameters of this estimator.

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

Fit Ridge regression model with cv.

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.



When sample_weight is provided, the selected hyperparameter may depend on whether we use leave-one-out cross-validation (cv=None or cv=’auto’) 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 parameters for this estimator.

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.


Parameter names mapped to their values.


Predict using the linear model.

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


Carray, shape (n_samples,)

Returns predicted values.

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

Return the coefficient of determination \(R^2\) of the prediction.

The coefficient \(R^2\) 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.

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.


\(R^2\) of self.predict(X) wrt. y.


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 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.


Estimator parameters.

selfestimator instance

Estimator instance.

Examples using sklearn.linear_model.RidgeCV