sklearn.linear_model
.BayesianRidge¶

class
sklearn.linear_model.
BayesianRidge
(*, n_iter=300, tol=0.001, alpha_1=1e06, alpha_2=1e06, lambda_1=1e06, lambda_2=1e06, 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_iterint, default=300
Maximum number of iterations. Should be greater than or equal to 1.
 tolfloat, default=1e3
Stop the algorithm if w has converged.
 alpha_1float, default=1e6
Hyperparameter : shape parameter for the Gamma distribution prior over the alpha parameter.
 alpha_2float, default=1e6
Hyperparameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter.
 lambda_1float, default=1e6
Hyperparameter : shape parameter for the Gamma distribution prior over the lambda parameter.
 lambda_2float, default=1e6
Hyperparameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter.
 alpha_initfloat, default=None
Initial value for alpha (precision of the noise). If not set, alpha_init is 1/Var(y).
New in version 0.22.
 lambda_initfloat, default=None
Initial value for lambda (precision of the weights). If not set, lambda_init is 1.
New in version 0.22.
 compute_scorebool, default=False
If True, compute the log marginal likelihood at each iteration of the optimization.
 fit_interceptbool, 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 (i.e. data is 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 l2norm. If you wish to standardize, please useStandardScaler
before callingfit
on an estimator withnormalize=False
. copy_Xbool, default=True
If True, X will be copied; else, it may be overwritten.
 verbosebool, default=False
Verbose mode when fitting the model.
 Attributes
 coef_arraylike of 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_arraylike of shape (n_features, n_features)
Estimated variancecovariance matrix of the weights
 scores_arraylike of 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
(X, y[, sample_weight])Fit the model
get_params
([deep])Get parameters for this estimator.
predict
(X[, return_std])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 the model
 Parameters
 Xndarray of shape (n_samples, n_features)
Training data
 yndarray of shape (n_samples,)
Target values. Will be cast to X’s dtype if necessary
 sample_weightndarray of shape (n_samples,), default=None
Individual weights for each sample
New in version 0.20: parameter sample_weight support to BayesianRidge.
 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
 paramsmapping of string to any
Parameter names mapped to their values.

predict
(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{arraylike, sparse matrix} of shape (n_samples, n_features)
Samples.
 return_stdbool, default=False
Whether to return the standard deviation of posterior prediction.
 Returns
 y_meanarraylike of shape (n_samples,)
Mean of predictive distribution of query points.
 y_stdarraylike of shape (n_samples,)
Standard deviation of predictive distribution of query points.

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  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
 Xarraylike 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, shape = (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
 yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for X.
 sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
R^2 of self.predict(X) wrt. y.
Notes
The R2 score used when calling
score
on a regressor usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).

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 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
 selfobject
Estimator instance.