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Title: Repulsive mixture models: Modelling and computations, with applications to high-dimensional data Authors:  Mario Beraha - Politecnico di Milano and Universita di Bologna (Italy) [presenting]
Lorenzo Ghilotti - Politecnico di Milano (Italy)
Alessandra Guglielmi - Politecnico di Milano (Italy)
Abstract: Bayesian mixture models offer a coherent framework for density estimation and model-based clustering. Usual formulations assume that, a priori, the cluster-specific parameters are i.i.d. from some base distribution, which may lead to estimating redundant clusters, especially when the model is misspecified. In repulsive mixtures, a joint prior for cluster-specific parameters is assumed, which puts higher mass on regular point patterns, i.e., well-separated configurations. Building on ideas from normalized random measures, we describe a general framework for repulsive mixture models, where a random probability measure is derived from a marked Gibbs point process with a (possibly unnormalized) density with respect to the unit rate Poisson point process. In particular, repulsiveness is encouraged among cluster-specific parameters while the unnormalized weights of the mixture arise from independent marks. When considering high-dimensional data, we show that repulsiveness can be incorporated into a latent factor model by means of an anisotropic point process and discuss specifically the case of determinantal point processes. We derive an MCMC sampler to simulate from the posterior distribution and validate our model on synthetic and real data.