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, alpha_init=None, lambda_init=None, compute_score=False, fit_intercept=True, normalize=False, copy_X=True, verbose=False)[source]

Bayesian ridge regression.

Fit a Bayesian ridge model. See the Notes section for details on this implementation and the optimization of the regularization parameters lambda (precision of the weights) and alpha (precision of the noise).

Read more in the User Guide.

Parameters:
n_iter : int, optional

Maximum number of iterations. Default is 300. Should be greater than or equal to 1.

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

alpha_init : float

Initial value for alpha (precision of the noise). If not set, alpha_init is 1/Var(y).

New in version 0.22.

lambda_init : float

Initial value for lambda (precision of the weights). If not set, lambda_init is 1.

New in version 0.22.

compute_score : boolean, optional

If True, compute the log marginal likelihood at each iteration of the optimization. Default is False.

fit_intercept : boolean, optional, default True

Whether to calculate the intercept for this model. The intercept is not treated as a probabilistic parameter and thus has no associated variance. If set to False, no intercept will be used in calculations (e.g. data is expected to be already centered).

normalize : boolean, optional, 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 sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.

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.

Attributes:
coef_ : array, shape = (n_features,)

Coefficients of the regression model (mean of distribution).

intercept_ : float

Independent term in decision function. Set to 0.0 if fit_intercept = False.

alpha_ : float

Estimated precision of the noise.

lambda_ : float

Estimated precision of the weights.

sigma_ : array, shape = (n_features, n_features)

Estimated variance-covariance matrix of the weights.

scores_ : array, shape = (n_iter_ + 1,)

If computed_score is True, value of the log marginal likelihood (to be maximized) at each iteration of the optimization. The array starts with the value of the log marginal likelihood obtained for the initial values of alpha and lambda and ends with the value obtained for the estimated alpha and lambda.

n_iter_ : int

The actual number of iterations to reach the stopping criterion.

Notes

There exist several strategies to perform Bayesian ridge regression. This implementation is based on the algorithm described in Appendix A of (Tipping, 2001) where updates of the regularization parameters are done as suggested in (MacKay, 1992). Note that according to A New View of Automatic Relevance Determination (Wipf and Nagarajan, 2008) these update rules do not guarantee that the marginal likelihood is increasing between two consecutive iterations of the optimization.

References

D. J. C. MacKay, Bayesian Interpolation, Computation and Neural Systems, Vol. 4, No. 3, 1992.

M. E. Tipping, Sparse Bayesian Learning and the Relevance Vector Machine, Journal of Machine Learning Research, Vol. 1, 2001.

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.BayesianRidge()
>>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
BayesianRidge()
>>> clf.predict([[1, 1]])
array([1.])

Methods

fit(self, X, y[, sample_weight]) Fit the model
get_params(self[, deep]) Get parameters for this estimator.
predict(self, X[, return_std]) Predict using the linear model.
score(self, X, y[, sample_weight]) Returns the coefficient of determination R^2 of the prediction.
set_params(self, \*\*params) Set the parameters of this estimator.
__init__(self, n_iter=300, tol=0.001, alpha_1=1e-06, alpha_2=1e-06, lambda_1=1e-06, lambda_2=1e-06, alpha_init=None, lambda_init=None, compute_score=False, fit_intercept=True, normalize=False, copy_X=True, verbose=False)[source]
fit(self, X, y, sample_weight=None)[source]

Fit the model

Parameters:
X : numpy array of shape [n_samples,n_features]

Training data

y : numpy array of shape [n_samples]

Target values. Will be cast to X’s dtype if necessary

sample_weight : numpy array of shape [n_samples]

Individual weights for each sample

New in version 0.20: parameter sample_weight support to BayesianRidge.

Returns:
self : returns an instance of self.
get_params(self, 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(self, X, return_std=False)[source]

Predict using the linear model.

In addition to the mean of the predictive distribution, also its standard deviation can be returned.

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

Samples.

return_std : boolean, optional

Whether to return the standard deviation of posterior prediction.

Returns:
y_mean : array, shape = (n_samples,)

Mean of predictive distribution of query points.

y_std : array, shape = (n_samples,)

Standard deviation of predictive distribution of query points.

score(self, 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 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, shape = (n_samples, n_features)

Test samples. For some estimators this may be a precomputed kernel matrix 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, 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.

Notes

The R2 score used when calling score on a regressor will use multioutput='uniform_average' from version 0.23 to keep consistent with metrics.r2_score. This will influence the score method of all the multioutput regressors (except for multioutput.MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call metrics.r2_score directly or make a custom scorer with metrics.make_scorer (the built-in scorer 'r2' uses multioutput='uniform_average').

set_params(self, **params)[source]

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.

Returns:
self