2023/06/19 by Andrea Cremaschi, Cremaschi, Andrea, Timothy Wertz +3 · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2306.10669
openalex publication_date 2023/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior distributions for the weights and location parameters of the mixture. Widely used are Bayesian semi-parametric models based on mixtures with infinite or random number of components, such as Dirichlet process mixtures or mixtures with random number of components. Key in this context is the choice of the kernel for cluster identification. Despite their popularity, the flexibility of these models and prior distributions often does not translate into interpretability of the identified clusters. To overcome this issue, clustering methods based on repulsive mixtures have been recently proposed. The basic idea is to include a repulsive term in the prior distribution of the atoms of the mixture, which favours mixture locations far apart. This approach is increasingly popular and allows one to produce well-separated clusters, thus facilitating the interpretation of the results. However, the resulting models are usually not easy to handle due to the introduction of unknown normalising constants. Exploiting results from statistical mechanics, we propose in this work a novel class of repulsive prior distributions based on Gibbs measures. Specifically, we use Gibbs measures associated to joint distributions of eigenvalues of random matrices, which naturally possess a repulsive property. The proposed framework greatly simplifies the computations needed for the use of repulsive mixtures due to the availability of the normalising constant in closed form. We investigate theoretical properties of such class of prior distributions, and illustrate the novel class of priors and their properties, as well as their clustering performance, on benchmark datasets.