3.2.4.1.9. sklearn.linear_model.RidgeCV¶

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)[source]¶

Ridge regression with built-in cross-validation.

See glossary entry for cross-validation estimator.

By default, it performs Generalized Cross-Validation, which is a form of efficient Leave-One-Out cross-validation.

Read more in the User Guide.

Parameters

alphasnumpy array of shape [n_alphas]

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 C^-1 in other linear models such as LogisticRegression or LinearSVC. If using generalized 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).

normalizeboolean, optional, 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 sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.

scoringstring, callable or None, optional, 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 generalized cross-validation), and r2 score otherwise.

cvint, cross-validation generator or an iterable, optional

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

• None, to use the efficient Leave-One-Out cross-validation (also known as Generalized 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, sklearn.model_selection.StratifiedKFold is used, else, sklearn.model_selection.KFold is used.

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

gcv_mode{None, ‘auto’, ‘svd’, eigen’}, optional

Flag indicating which strategy to use when performing Generalized 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_valuesboolean, 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 Generalized Cross-Validation).

Attributes

cv_values_array, shape = [n_samples, n_alphas] or shape = [n_samples, n_targets, n_alphas], optional

Cross-validation values for each alpha (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_array, shape = [n_features] or [n_targets, n_features]

Weight vector(s).

intercept_float | array, shape = (n_targets,)

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

alpha_float

Estimated regularization parameter.

See also

Ridge

Ridge regression

RidgeClassifier

Ridge classifier

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...

Methods

fit(self, X, y[, sample_weight])	Fit Ridge regression model
get_params(self[, deep])	Get parameters for this estimator.
predict(self, X)	Predict using the linear model
score(self, X, y[, sample_weight])	Returns the coefficient of determination R^2 of the prediction.
set_params(self, \*\*params)	Set the parameters of this estimator.

__init__(self, alphas=(0.1, 1.0, 10.0), fit_intercept=True, normalize=False, scoring=None, cv=None, gcv_mode=None, store_cv_values=False)[source]¶

Initialize self. See help(type(self)) for accurate signature.

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

Fit Ridge regression model

Parameters

Xarray-like, shape = [n_samples, n_features]

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

yarray-like, shape = [n_samples] or [n_samples, n_targets]

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

sample_weightfloat or array-like of shape [n_samples]

Sample weight

Returns

selfobject

Notes

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

get_params(self, deep=True)[source]¶

Get parameters for this estimator.

Parameters

deepboolean, optional

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

Returns

paramsmapping of string to any

Parameter names mapped to their values.

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

Returns the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - 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, shape = (n_samples, n_features)

Test samples. For some estimators this may be a precomputed kernel matrix instead, shape = (n_samples, n_samples_fitted], where n_samples_fitted is the number of samples used in the fitting for the estimator.

yarray-like, shape = (n_samples) or (n_samples, n_outputs)

True values for X.

sample_weightarray-like, shape = [n_samples], optional

Sample weights.

Returns

scorefloat

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

Notes

The R2 score used when calling score on a regressor will use multioutput='uniform_average' from version 0.23 to keep consistent with r2_score. This will influence the score method of all the multioutput regressors (except for MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call r2_score directly or make a custom scorer with make_scorer (the built-in scorer 'r2' uses multioutput='uniform_average').

set_params(self, **params)[source]¶

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns

self

3.2.4.1.9.1. Examples using sklearn.linear_model.RidgeCV¶

Combine predictors using stacking¶