8.14.1.2. sklearn.linear_model.Ridge

class sklearn.linear_model.Ridge(alpha=1.0, fit_intercept=True, normalize=False, copy_X=True, tol=0.001)

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_responses]).

Parameters :

alpha : float

Small positive values of alpha improve the conditioning of the problem and reduce the variance of the estimates. Alpha corresponds to (2*C)^-1 in other linear models such as LogisticRegression or LinearSVC.

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).

normalize : boolean, optional

If True, the regressors X are normalized

copy_X : boolean, optional, default True

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

tol: float :

Precision of the solution.

See also

RidgeClassifier, RidgeCV

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, normalize=False,
   tol=0.001)

Attributes

coef_

array, shape = [n_features] or [n_responses, n_features]

Weight vector(s).

Methods

decision_function(X)	Decision function of the linear model
fit(X, y[, sample_weight, solver])	Fit Ridge regression model
predict(X)	Predict using the linear model
score(X, y)	Returns the coefficient of determination R^2 of the prediction.
set_params(**params)	Set the parameters of the estimator.

__init__(alpha=1.0, fit_intercept=True, normalize=False, copy_X=True, tol=0.001)

decision_function(X)

Decision function of the linear model

Parameters :

X : numpy array of shape [n_samples, n_features]

Returns :

C : array, shape = [n_samples]

Returns predicted values.

fit(X, y, sample_weight=1.0, solver='auto')

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_responses]

Target values

sample_weight : float or numpy array of shape [n_samples]

Individual weights for each sample

solver : {‘auto’, ‘dense_cholesky’, ‘sparse_cg’}

Solver to use in the computational routines. ‘delse_cholesky’ will use the standard scipy.linalg.solve function, ‘sparse_cg’ will use the a conjugate gradient solver as found in scipy.sparse.linalg.cg while ‘auto’ will chose the most appropiate depending on the matrix X.

Returns :

self : returns an instance of self.

predict(X)

Predict using the linear model

Parameters :

X : numpy array of shape [n_samples, n_features]

Returns :

C : array, shape = [n_samples]

Returns predicted values.

score(X, y)

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 - 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, lower values are worse.

Parameters :

X : array-like, shape = [n_samples, n_features]

Training set.

y : array-like, shape = [n_samples]

Returns :

z : float

set_params(**params)

Set the parameters of the 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.

Returns :self :