Repulsive Mixture Model with Projection Determinantal Point Process

2025-10-09

AI Summary

In Bayesian mixture models, independently specified priors on cluster centers often induce component overlap, undermining interpretability; existing repulsive priors suffer from computational intractability and theoretical intractability. This paper proposes a repulsive mixture model based on the projection determinantal point process (DPP), the first fully tractable and exactly samplable repulsive prior. We derive closed-form posterior and predictive distributions analytically, design efficient conditional Gibbs and marginal sampling algorithms, and establish frequentist consistency guarantees. Experiments demonstrate that our model significantly outperforms existing methods under model misspecification and successfully identifies neurocognitively meaningful, interpretable subgroups in event-related potential data.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In many scientific domains, clustering aims to reveal interpretable latent structure that reflects relevant subpopulations or processes. Widely used Bayesian mixture models for model-based clustering often produce overlapping or redundant components because priors on cluster locations are specified independently, hindering interpretability. To mitigate this, repulsive priors have been proposed to encourage well-separated components, yet existing approaches face both computational and theoretical challenges. We introduce a fully tractable Bayesian repulsive mixture model by assigning a projection Determinantal Point Process (DPP) prior to the component locations. Projection DPPs induce strong repulsion and allow exact sampling, enabling parsimonious and interpretable posterior clustering. Leveraging their analytical tractability, we derive closed-form posterior and predictive distributions. These results, in turn, enable two efficient inference algorithms: a conditional Gibbs sampler and the first fully implementable marginal sampler for DPP-based mixtures. We also provide strong frequentist guarantees, including posterior consistency for density estimation, elimination of redundant components, and contraction of the mixing measure. Simulation studies confirm superior mixing and clustering performance compared to alternatives in misspecified settings. Finally, we demonstrate the utility of our method on event-related potential functional data, where it uncovers interpretable neuro-cognitive subgroups. Our results support the projection DPP mixtures as a theoretically sound and practically effective solution for Bayesian clustering.

Problem

• Develops tractable Bayesian repulsive mixture model
• Addresses overlapping components in clustering interpretability
• Enables exact sampling and efficient inference algorithms

Innovation

• Projection DPP prior induces strong repulsion
• Enables exact sampling and closed-form distributions
• Provides efficient Gibbs and marginal samplers