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_iterint, default=300 

Maximum number of iterations. Should be greater than or equal to 1.  
tolfloat, default=1e-3 

Stop the algorithm if w has converged.  
alpha_1float, default=1e-6 

Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter.  
alpha_2float, default=1e-6 

Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter.  
lambda_1float, default=1e-6 

Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter.  
lambda_2float, default=1e-6 

Hyper-parameter : 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 l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=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_array-like 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_array-like of shape (n_features, n_features) 

Estimated variance-covariance matrix of the weights  
scores_array-like 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.  
X_offset_float 

If normalize=True, offset subtracted for centering data to a zero mean.  
X_scale_float 

If normalize=True, parameter used to scale data to a unit standard deviation.     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 
 
paramsdict 

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{array-like, sparse matrix} of shape (n_samples, n_features) 

Samples.  
return_stdbool, default=False 

Whether to return the standard deviation of posterior prediction.    Returns 
 
y_meanarray-like of shape (n_samples,) 

Mean of predictive distribution of query points.  
y_stdarray-like 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 \((1 - \frac{u}{v})\), 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 
 
Xarray-like 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 with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.  
yarray-like of shape (n_samples,) or (n_samples, n_outputs) 

True values for X.  
sample_weightarray-like of shape (n_samples,), default=None 

Sample weights.    Returns 
 
scorefloat 

\(R^2\) of self.predict(X) wrt. y.     Notes The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor). 
  
set_params(**params) [source]
 
Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as Pipeline). 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 
 
selfestimator instance 

Estimator instance.     
 
 Examples using sklearn.linear_model.BayesianRidge
 
  Feature agglomeration vs. univariate selection  

  Curve Fitting with Bayesian Ridge Regression  

  Bayesian Ridge Regression  

  Imputing missing values with variants of IterativeImputer