package sklearn

Ridge regression with built-in cross-validation.

See glossary entry for :term:`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 :ref:`User Guide <ridge_regression>`.

Parameters ---------- alphas : ndarray 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 ``C^-1`` in other linear models such as LogisticRegression or LinearSVC. If using generalized cross-validation, alphas must be positive.

fit_intercept : bool, 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).

normalize : bool, 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 :class:`sklearn.preprocessing.StandardScaler` before calling ``fit`` on an estimator with ``normalize=False``.

scoring : string, 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 generalized cross-validation), and r2 score otherwise.

cv : int, 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 (also known as Generalized Cross-Validation).
• integer, to specify the number of folds.
• :term:`CV splitter`,
• An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, if ``y`` is binary or multiclass, :class:`sklearn.model_selection.StratifiedKFold` is used, else, :class:`sklearn.model_selection.KFold` is used.

Refer :ref:`User Guide <cross_validation>` 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 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_values : bool, 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_ : ndarray of 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_ : 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 Estimated regularization parameter.

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...

See also -------- Ridge : Ridge regression RidgeClassifier : Ridge classifier RidgeClassifierCV : Ridge classifier with built-in cross validation

Fit Ridge regression model with cv.

Parameters ---------- X : ndarray of shape (n_samples, n_features) Training data. If using GCV, will be cast to float64 if necessary.

y : ndarray of shape (n_samples,) or (n_samples, n_targets) Target values. Will be cast to X's dtype if necessary.

sample_weight : float or ndarray of shape (n_samples,), default=None Individual weights for each sample. If given a float, every sample will have the same weight.

Returns ------- self : object

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 parameters for this estimator.

Parameters ---------- deep : bool, default=True If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns ------- params : mapping of string to any Parameter names mapped to their values.

Predict using the linear model.

Parameters ---------- X : array_like or sparse matrix, shape (n_samples, n_features) Samples.

Returns ------- C : array, shape (n_samples,) Returns predicted values.

Return 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 ---------- X : array-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, shape = (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

y : array-like of shape (n_samples,) or (n_samples, n_outputs) True values for X.

sample_weight : array-like of shape (n_samples,), default=None Sample weights.

Returns ------- score : float 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 :func:`~sklearn.metrics.r2_score`. This will influence the ``score`` method of all the multioutput regressors (except for :class:`~sklearn.multioutput.MultiOutputRegressor`). To specify the default value manually and avoid the warning, please either call :func:`~sklearn.metrics.r2_score` directly or make a custom scorer with :func:`~sklearn.metrics.make_scorer` (the built-in scorer ``'r2'`` uses ``multioutput='uniform_average'``).

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.

Parameters ---------- **params : dict Estimator parameters.

Returns ------- self : object Estimator instance.

Attribute cv_values_: get value or raise Not_found if None.

Attribute cv_values_: get value as an option.

Attribute coef_: get value or raise Not_found if None.

Attribute coef_: get value as an option.

Attribute intercept_: get value or raise Not_found if None.

Attribute intercept_: get value as an option.

Attribute alpha_: get value or raise Not_found if None.

Attribute alpha_: get value as an option.

Print the object to a human-readable representation.

Print the object to a human-readable representation.

Pretty-print the object to a formatter.