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Bayesian Sparse Gaussian Mixture Model for Clustering in High Dimensions.

Dapeng Yao¹, Fangzheng Xie², Yanxun Xu¹

¹Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland, U.S.A.

Journal of Machine Learning Research : JMLR

|March 9, 2026

Summary

This summary is machine-generated.

This study introduces a computationally tractable Bayesian approach for sparse high-dimensional Gaussian mixture models. The method achieves minimax optimal estimation rates and adaptively estimates the number of clusters, outperforming traditional methods.

Keywords:

Clustering High dimensions Minimax estimation Posterior contraction Single-cell sequencing

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Area of Science:

Statistics
Machine Learning
Computational Biology

Background:

High-dimensional Gaussian mixture models are widely used for clustering.
Traditional methods face computational intractability and require pre-specifying the number of clusters.
Growing number of clusters with sample size poses challenges in parameter estimation.

Purpose of the Study:

To develop a computationally tractable Bayesian approach for sparse high-dimensional Gaussian mixture models.
To establish minimax lower bounds for parameter estimation in this setting.
To demonstrate adaptive estimation of the number of clusters.

Main Methods:

Proposed a Bayesian approach using a continuous spike-and-slab prior for sparse cluster centers.
Established minimax lower bounds for parameter estimation.
Proved posterior contraction rates and derived mis-clustering rates using matrix perturbation theory.

Main Results:

The proposed Bayesian method achieves minimax optimal posterior contraction rates.
The method adaptively estimates the number of clusters without pre-specification.
Demonstrated validity and usefulness through simulations and single-cell RNA sequencing data analysis.

Conclusions:

The proposed Bayesian sparse Gaussian mixture model offers a computationally tractable and statistically robust solution.
The method effectively handles high-dimensional data and adaptively determines cluster numbers.
Applicable to real-world problems, including single-cell RNA sequencing analysis.