sklearn.linear_model.Ridge

class sklearn.linear_model.Ridge(alpha=1.0, *, fit_intercept=True, normalize='deprecated', copy_X=True, max_iter=None, tol=0.001, solver='auto', random_state=None)[source]

Linear least squares with l2 regularization.

Minimizes the objective function:

||y - Xw||^2_2 + alpha * ||w||^2_2

This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm. Also known as Ridge Regression or Tikhonov regularization. This estimator has built-in support for multi-variate regression (i.e., when y is a 2d-array of shape (n_samples, n_targets)).

Read more in the User Guide.

Parameters
alpha{float, ndarray of shape (n_targets,)}, default=1.0

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 an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number.

fit_interceptbool, default=True

Whether to fit the intercept for this model. If set to false, no intercept will be used in calculations (i.e. X and y are 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.

Deprecated since version 1.0: normalize was deprecated in version 1.0 and will be removed in 1.2.

copy_Xbool, default=True

If True, X will be copied; else, it may be overwritten.

max_iterint, default=None

Maximum number of iterations for conjugate gradient solver. For ‘sparse_cg’ and ‘lsqr’ solvers, the default value is determined by scipy.sparse.linalg. For ‘sag’ solver, the default value is 1000.

tolfloat, default=1e-3

Precision of the solution.

solver{‘auto’, ‘svd’, ‘cholesky’, ‘lsqr’, ‘sparse_cg’, ‘sag’, ‘saga’}, default=’auto’

Solver to use in the computational routines:

  • ‘auto’ chooses the solver automatically based on the type of data.

  • ‘svd’ uses a Singular Value Decomposition of X to compute the Ridge coefficients. More stable for singular matrices than ‘cholesky’.

  • ‘cholesky’ uses the standard scipy.linalg.solve function to obtain a closed-form solution.

  • ‘sparse_cg’ uses the conjugate gradient solver as found in scipy.sparse.linalg.cg. As an iterative algorithm, this solver is more appropriate than ‘cholesky’ for large-scale data (possibility to set tol and max_iter).

  • ‘lsqr’ uses the dedicated regularized least-squares routine scipy.sparse.linalg.lsqr. It is the fastest and uses an iterative procedure.

  • ‘sag’ uses a Stochastic Average Gradient descent, and ‘saga’ uses its improved, unbiased version named SAGA. Both methods also use an iterative procedure, and are often faster than other solvers when both n_samples and n_features are large. Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.

All last five solvers support both dense and sparse data. However, only ‘sag’ and ‘sparse_cg’ supports sparse input when fit_intercept is True.

New in version 0.17: Stochastic Average Gradient descent solver.

New in version 0.19: SAGA solver.

random_stateint, RandomState instance, default=None

Used when solver == ‘sag’ or ‘saga’ to shuffle the data. See Glossary for details.

New in version 0.17: random_state to support Stochastic Average Gradient.

Attributes
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.

n_iter_None or ndarray of shape (n_targets,)

Actual number of iterations for each target. Available only for sag and lsqr solvers. Other solvers will return None.

New in version 0.17.

n_features_in_int

Number of features seen during fit.

New in version 0.24.

See also

RidgeClassifier

Ridge classifier.

RidgeCV

Ridge regression with built-in cross validation.

KernelRidge

Kernel ridge regression combines ridge regression with the kernel trick.

Examples

>>> from sklearn.linear_model import Ridge
>>> import numpy as np
>>> n_samples, n_features = 10, 5
>>> rng = np.random.RandomState(0)
>>> y = rng.randn(n_samples)
>>> X = rng.randn(n_samples, n_features)
>>> clf = Ridge(alpha=1.0)
>>> clf.fit(X, y)
Ridge()

Methods

fit(X, y[, sample_weight])

Fit Ridge regression model.

get_params([deep])

Get parameters for this estimator.

predict(X)

Predict using the linear model.

score(X, y[, sample_weight])

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

set_params(**params)

Set the parameters of this estimator.

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

Fit Ridge regression model.

Parameters
X{ndarray, sparse matrix} of shape (n_samples, n_features)

Training data

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

Target values

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.

Returns
selfreturns an instance of self.
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, shape (n_samples, n_features)

Samples.

Returns
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.

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) wrt. 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_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.

Examples using sklearn.linear_model.Ridge