Bayesian Repulsive Mixture Modeling with Mat\'ern Point Processes

TL;DR

This paper introduces a Bayesian mixture model with repulsion between components using a Matérn point process, improving cluster separation and interpretability, with efficient inference via a novel Gibbs sampler.

Contribution

It proposes a new Bayesian mixture model incorporating repulsion through a Matérn point process, enabling efficient inference and cluster number estimation.

Findings

Effective separation of overlapping clusters

Robustness to poorly separated data

Successful application on synthetic and real data

Abstract

Mixture models are a standard tool in statistical analyses, widely used for density modeling and model-based clustering. In this work, we propose a Bayesian mixture model with repulsion between mixture components. Such repulsion helps address the problem of overlapping or poorly separated clusters, and assists with model interpretibility and robustness. Our modeling approach introduces repulsion via a generalized Mat\'ern type-III repulsive point process model, and proceeds by applying a dependent sequential thinning scheme to a latent Poisson point process. A key feature of our model is that in contrast to most existing approaches to modeling repulsion, efficient posterior inference is possible via a Gibbs sampler, one that exploits the latent Poisson of our problem. This novel sampler also allows posterior inference over the number of clusters, and is of independent interest even in standard clustering applications without repulsion. We demonstrate the utility of the proposed method on a number of synthetic and real-world problems.