Implementation:Scikit learn Scikit learn BayesianRidge

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Bayesian Regression
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for Bayesian ridge regression with automatic regularization parameter tuning provided by scikit-learn.

Description

BayesianRidge implements Bayesian ridge regression, fitting a Bayesian ridge model by optimizing the regularization parameters lambda (precision of the weights) and alpha (precision of the noise). The model places Gamma priors over the alpha and lambda parameters and iteratively updates them using evidence maximization (type-II maximum likelihood). This approach automatically determines the optimal regularization strength from the data itself, unlike standard ridge regression where the regularization parameter must be set manually.

Usage

Use BayesianRidge when you need a regression model that automatically tunes its regularization strength, when you want uncertainty estimates on predictions, or when you want to compute the log marginal likelihood for model comparison. It is particularly useful when you have limited data and want to avoid overfitting without manual hyperparameter tuning.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/linear_model/_bayes.py

Signature

class BayesianRidge(RegressorMixin, LinearModel):
    def __init__(
        self,
        *,
        max_iter=300,
        tol=1e-3,
        alpha_1=1e-6,
        alpha_2=1e-6,
        lambda_1=1e-6,
        lambda_2=1e-6,
        alpha_init=None,
        lambda_init=None,
        compute_score=False,
        fit_intercept=True,
        copy_X=True,
        verbose=False,
    ):

Import

from sklearn.linear_model import BayesianRidge

I/O Contract

Inputs

Name	Type	Required	Description
max_iter	int	No	Maximum number of iterations over the complete dataset (default=300)
tol	float	No	Convergence threshold for stopping the algorithm (default=1e-3)
alpha_1	float	No	Shape parameter for the Gamma distribution prior over alpha (default=1e-6)
alpha_2	float	No	Inverse scale parameter for the Gamma distribution prior over alpha (default=1e-6)
lambda_1	float	No	Shape parameter for the Gamma distribution prior over lambda (default=1e-6)
lambda_2	float	No	Inverse scale parameter for the Gamma distribution prior over lambda (default=1e-6)
alpha_init	float	No	Initial value for alpha (precision of noise); defaults to 1/Var(y)
lambda_init	float	No	Initial value for lambda (precision of weights); defaults to 1
compute_score	bool	No	Whether to compute log marginal likelihood at each iteration (default=False)
fit_intercept	bool	No	Whether to calculate the intercept (default=True)
copy_X	bool	No	Whether to copy X (default=True)

Outputs

Name	Type	Description
coef_	ndarray of shape (n_features,)	Coefficients of the regression model
intercept_	float	Estimated independent term in the linear model
alpha_	float	Estimated precision of the noise
lambda_	float	Estimated precision of the weights
sigma_	ndarray of shape (n_features, n_features)	Estimated variance-covariance matrix of the weights
scores_	array-like of shape (n_iter_+1,)	Log marginal likelihood at each iteration (if compute_score=True)

Usage Examples

Basic Usage

from sklearn.linear_model import BayesianRidge
from sklearn.datasets import make_regression

X, y = make_regression(n_samples=100, n_features=10, noise=10, random_state=42)
model = BayesianRidge()
model.fit(X, y)
predictions = model.predict(X)
print("Alpha:", model.alpha_)
print("Lambda:", model.lambda_)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Bayesian_Regression