Implementation:Scikit learn Scikit learn BayesianGaussianMixture

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Mixture Models, Bayesian Inference
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for variational Bayesian estimation of a Gaussian mixture model provided by scikit-learn.

Description

BayesianGaussianMixture infers an approximate posterior distribution over the parameters of a Gaussian mixture distribution using variational inference. Unlike GaussianMixture, it can automatically determine the effective number of components from the data by using a Dirichlet process or Dirichlet distribution prior on the mixture weights. Components with near-zero weight are effectively pruned. It extends BaseMixture and uses Wishart priors on precision matrices and normal priors on means.

Usage

Use BayesianGaussianMixture when the number of mixture components is unknown and should be inferred from the data, or when you want to incorporate prior knowledge about the mixture distribution. It is well-suited for density estimation, soft clustering, and situations where a fully Bayesian treatment of uncertainty is desirable.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/mixture/_bayesian_mixture.py

Signature

class BayesianGaussianMixture(BaseMixture):
    def __init__(
        self,
        *,
        n_components=1,
        covariance_type="full",
        tol=1e-3,
        reg_covar=1e-6,
        max_iter=100,
        n_init=1,
        init_params="kmeans",
        weight_concentration_prior_type="dirichlet_process",
        weight_concentration_prior=None,
        mean_precision_prior=None,
        mean_prior=None,
        degrees_of_freedom_prior=None,
        covariance_prior=None,
        random_state=None,
        warm_start=False,
        verbose=0,
        verbose_interval=10,
    ):

Import

from sklearn.mixture import BayesianGaussianMixture

I/O Contract

Inputs

Name	Type	Required	Description
n_components	int	No	Maximum number of mixture components. Effective number may be smaller. Default is 1.
covariance_type	str	No	Covariance parameter type: "full", "tied", "diag", or "spherical". Default is "full".
tol	float	No	Convergence threshold. Default is 1e-3.
reg_covar	float	No	Regularization added to covariance diagonal. Default is 1e-6.
max_iter	int	No	Maximum number of variational inference iterations. Default is 100.
n_init	int	No	Number of initializations. Default is 1.
init_params	str	No	Initialization method: "kmeans", "random", "random_from_data", or "k-means++". Default is "kmeans".
weight_concentration_prior_type	str	No	Prior type: "dirichlet_process" or "dirichlet_distribution". Default is "dirichlet_process".
weight_concentration_prior	float or None	No	Concentration parameter for the weight distribution prior. Default is None.
mean_precision_prior	float or None	No	Precision prior on the mean distribution. Default is None.
mean_prior	array-like or None	No	Prior on the mean distribution. Default is None.
degrees_of_freedom_prior	float or None	No	Prior degrees of freedom on the covariance Wishart distribution. Default is None.
covariance_prior	float, array-like, or None	No	Prior on the covariance distribution. Default is None.
random_state	int or RandomState	No	Random state for reproducibility. Default is None.
warm_start	bool	No	Whether to use solution of last fit as initialization. Default is False.
verbose	int	No	Verbosity level. Default is 0.
verbose_interval	int	No	Interval between verbose log messages. Default is 10.

Outputs

Name	Type	Description
weights_	ndarray of shape (n_components,)	Weight of each mixture component.
means_	ndarray of shape (n_components, n_features)	Mean of each mixture component.
covariances_	ndarray	Covariance of each mixture component (shape depends on covariance_type).
precisions_	ndarray	Precision matrices for each component.
precisions_cholesky_	ndarray	Cholesky decomposition of the precision matrices.
converged_	bool	Whether variational inference converged.
n_iter_	int	Number of iterations performed.
lower_bound_	float	Lower bound value on the model evidence (ELBO).
weight_concentration_	ndarray or tuple	Dirichlet concentration parameters of the weight distribution.
mean_precision_	ndarray of shape (n_components,)	Precision parameter for each component's mean.
degrees_of_freedom_	ndarray of shape (n_components,)	Degrees of freedom of each component's Wishart distribution.

Usage Examples

Basic Usage

from sklearn.mixture import BayesianGaussianMixture
import numpy as np

X = np.array([[1, 2], [1, 4], [1, 0],
              [10, 2], [10, 4], [10, 0]])

bgm = BayesianGaussianMixture(n_components=5, random_state=42).fit(X)
print(bgm.predict(X))
print(bgm.weights_)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Density_Estimation