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Title: Repulsion, chaos and equilibrium in mixture models Authors:  Maria De Iorio - National University of Singapore (Singapore) [presenting]
Abstract: Mixture models are commonly used in applications presenting heterogeneity and overdispersion in the population. In the Bayesian framework, this entails the specification of suitable prior distributions for the weights and location parameters of the mixture. Indeed, 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 leads to 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 intractable normalising constants. Exploiting results from statistical mechanics, we propose a novel class of repulsive prior distributions based on Gibbs's measures. Specifically, we use Gibbs measures associated with joint distributions of eigenvalues of random matrices, which naturally possess a repulsive property. The proposed framework greatly simplifies computations, due to the availability of the normalising constant in closed form. We establish theoretical results that imply that the locations become independent as the number of components tends to infinity and illustrate the novel class of priors on benchmark datasets.