B0368
Title: Repulsion, chaos and equilibrium in mixture models
Authors: Andrea Cremaschi - ASTAR (Singapore) [presenting]
Maria De Iorio - National University of Singapore (Singapore)
Timothy Wertz - National University of Singapore (Singapore)
Abstract: Mixture models are commonly used to analyse data presenting heterogeneity and overdispersion, 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 numbers of components. Often, the flexibility of these models does not translate into the interpretability of the identified clusters. To overcome this issue, clustering methods based on repulsive mixtures have been recently proposed, including a repulsive term in the prior distribution of the atoms of the mixture, favouring locations far apart. This approach is increasingly popular and allows to production of 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, a novel class of repulsive prior distributions is proposed based on Gibbs measures associated with joint distributions of eigenvalues of random matrices, which naturally possess a repulsive property. The proposed framework greatly simplifies the computations needed due to the availability of the normalising constant in closed form. The novel class of priors and their properties are illustrated as well as their clustering performance, on benchmark datasets.
