8.14.1.17. sklearn.linear_model.BayesianRidge

class sklearn.linear_model.BayesianRidge(n_iter=300, tol=0.001, alpha_1=1e-06, alpha_2=1e-06, lambda_1=1e-06, lambda_2=1e-06, compute_score=False, fit_intercept=True, normalize=False, copy_X=True, verbose=False)

Bayesian ridge regression

Fit a Bayesian ridge model and optimize the regularization parameters lambda (precision of the weights) and alpha (precision of the noise).

Parameters :

X : array, shape = (n_samples, n_features)

Training vectors.

y : array, shape = (length)

Target values for training vectors

n_iter : int, optional

Maximum number of iterations. Default is 300.

tol : float, optional

Stop the algorithm if w has converged. Default is 1.e-3.

alpha_1 : float, optional

Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter. Default is 1.e-6

alpha_2 : float, optional

Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter. Default is 1.e-6.

lambda_1 : float, optional

Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter. Default is 1.e-6.

lambda_2 : float, optional

Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter. Default is 1.e-6

compute_score : boolean, optional

If True, compute the objective function at each step of the model. Default is False

fit_intercept : boolean, optional

wether 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). Default is True.

normalize : boolean, optional, default False

If True, the regressors X are normalized

copy_X : boolean, optional, default True

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

verbose : boolean, optional, default False

Verbose mode when fitting the model.

Notes

See examples/linear_model/plot_bayesian_ridge.py for an example.

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.BayesianRidge()
>>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
... 
BayesianRidge(alpha_1=1e-06, alpha_2=1e-06, compute_score=False,
        copy_X=True, fit_intercept=True, lambda_1=1e-06, lambda_2=1e-06,
        n_iter=300, normalize=False, tol=0.001, verbose=False)
>>> clf.predict([[1, 1]])
array([ 1.])

Attributes

coef_	array, shape = (n_features)	Coefficients of the regression model (mean of distribution)
alpha_	float	estimated precision of the noise.
lambda_	array, shape = (n_features)	estimated precisions of the weights.
scores_	float	if computed, value of the objective function (to be maximized)

Methods

decision_function(X)	Decision function of the linear model
fit(X, y)	Fit the 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__(n_iter=300, tol=0.001, alpha_1=1e-06, alpha_2=1e-06, lambda_1=1e-06, lambda_2=1e-06, compute_score=False, fit_intercept=True, normalize=False, copy_X=True, verbose=False)

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)

Fit the model

Parameters :

X : numpy array of shape [n_samples,n_features]

Training data

y : numpy array of shape [n_samples]

Target values

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 :