`sklearn.linear_model`.Ridge¶

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

Linear least squares with l2 regularization.

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, array-like}, shape (n_targets)

Small positive values of alpha improve the conditioning of the problem and reduce the variance of the estimates. Alpha corresponds to C^-1 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.

copy_X : boolean, optional, default True

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

fit_intercept : boolean

Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).

max_iter : int, optional

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.

normalize : boolean, optional, default False

If True, the regressors X will be normalized before regression.

solver : {‘auto’, ‘svd’, ‘cholesky’, ‘lsqr’, ‘sparse_cg’, ‘sag’}

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 but may not be available in old scipy versions. It also uses an iterative procedure.

‘sag’ uses a Stochastic Average Gradient descent. It also uses an iterative procedure, and is often faster than other solvers when both n_samples and n_features are large. Note that ‘sag’ 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 four solvers support both dense and sparse data. However, only ‘sag’ supports sparse input when fit_intercept is True.

New in version 0.17: Stochastic Average Gradient descent solver.

tol : float

Precision of the solution.

random_state : int seed, RandomState instance, or None (default)

The seed of the pseudo random number generator to use when shuffling the data. Used only in ‘sag’ solver.

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

Attributes:

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.

n_iter_ : array or None, shape (n_targets,)

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

See also

RidgeClassifier, RidgeCV, KernelRidge

Examples

>>> from sklearn.linear_model import Ridge
>>> import numpy as np
>>> n_samples, n_features = 10, 5
>>> np.random.seed(0)
>>> y = np.random.randn(n_samples)
>>> X = np.random.randn(n_samples, n_features)
>>> clf = Ridge(alpha=1.0)
>>> clf.fit(X, y) 
Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)

Methods

`decision_function`(args, *kwargs)	DEPRECATED: and will be removed in 0.19.
`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])	Returns the coefficient of determination R^2 of the prediction.
`set_params`(**params)	Set the parameters of this estimator.

__init__(alpha=1.0, fit_intercept=True, normalize=False, copy_X=True, max_iter=None, tol=0.001, solver='auto', random_state=None)[source]¶

decision_function(*args, **kwargs)[source]¶

DEPRECATED: and will be removed in 0.19.

Decision function of the linear model.

Parameters:

X : {array-like, sparse matrix}, shape = (n_samples, n_features)

Samples.

Returns:

C : array, shape = (n_samples,)

Returns predicted values.

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

Fit Ridge regression model

Parameters:

X : {array-like, sparse matrix}, shape = [n_samples, n_features]

Training data

y : array-like, shape = [n_samples] or [n_samples, n_targets]

Target values

sample_weight : float or numpy array of shape [n_samples]

Individual weights for each sample

Returns:

self : returns an instance of self.

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters:

deep: boolean, optional :

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(X)[source]¶

Predict using the linear model

Parameters:

X : {array-like, sparse matrix}, shape = (n_samples, n_features)

Samples.

Returns:

C : array, shape = (n_samples,)

Returns predicted values.

score(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 regression sum of squares ((y_true - y_pred) ** 2).sum() and v is the residual sum of squares ((y_true - y_true.mean()) ** 2).sum(). 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, shape = (n_samples, n_features)

Test samples.

y : array-like, shape = (n_samples) or (n_samples, n_outputs)

True values for X.

sample_weight : array-like, shape = [n_samples], optional

Sample weights.

Returns:

score : float

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

set_params(**params)[source]¶

Set the parameters of this estimator.

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