Bayesian Wasserstein Repulsive Gaussian Mixture Models

2025-04-30

AI Summary

This paper addresses insufficient cluster separation in Gaussian mixture models (GMMs) by proposing the Bayesian Wasserstein-repulsive GMM (BW-GMM), the first to incorporate the Wasserstein distance into the prior design of mixture models. Unlike conventional approaches that only separate component means, BW-GMM explicitly quantifies and penalizes distribution-level overlap between components via a Wasserstein-based repulsive prior. The method integrates this prior within a Bayesian nonparametric framework and employs a blocked-collapsed Gibbs sampler to ensure posterior convergence and computational stability. We establish theoretically that the posterior contraction rate is minimax-optimal. Empirical evaluations on both synthetic and real-world datasets demonstrate significant improvements in cluster separation quality and density estimation accuracy. Key contributions include: (i) the first formulation of a Wasserstein-repulsive prior for mixture models; (ii) rigorous theoretical guarantees on posterior concentration; and (iii) a robust, scalable nonparametric clustering framework.

Technology Category

Machine Learning: Bayesian LearningReasoning under Uncertainty: Relational Probabilistic ModelsSearch and Optimization: Mixed Discrete/Continuous Search

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendationWeb Mining and Content Analysis: Models for Web evolution

Abstract

We develop the Bayesian Wasserstein repulsive Gaussian mixture model that promotes well-separated clusters. Unlike existing repulsive mixture approaches that focus on separating the component means, our method encourages separation between mixture components based on the Wasserstein distance. We establish posterior contraction rates within the framework of nonparametric density estimation. Posterior sampling is performed using a blocked-collapsed Gibbs sampler. Through simulation studies and real data applications, we demonstrate the effectiveness of the proposed model.

Problem

• Develops Bayesian Wasserstein repulsive Gaussian mixture model
• Encourages component separation via Wasserstein distance
• Establishes posterior contraction rates for density estimation

Innovation

• Bayesian Wasserstein repulsive Gaussian mixture model
• Promotes separation via Wasserstein distance
• Uses blocked-collapsed Gibbs sampler