A0984
Title: Repulsive mixtures via the sparsity-inducing partition prior
Authors: Alexander Mozdzen - A*STAR (Singapore) [presenting]
Gregor Kastner - University of Klagenfurt (Austria)
Andrea Cremaschi - IE University (Spain)
Maria De Iorio - National University of Singapore (Singapore)
Timothy Wertz - National University of Singapore (Singapore)
Abstract: A novel prior distribution is introduced for modelling the weights in mixture models based on a generalization of the Dirichlet distribution, the Selberg Dirichlet distribution. The prior contains a repulsive term, which naturally penalises values that lie close to each other on the simplex, thus encouraging few dominating clusters. The repulsive behaviour induces additional sparsity in the number of components. This construction is referred to as a sparsity-inducing partition (SIP) prior. By highlighting differences with the conventional Dirichlet distribution, relevant properties of the SIP prior are presented, and their implications are demonstrated across a variety of mixture models, including finite mixtures with a fixed or random number of components as well as repulsive mixtures. An efficient posterior sampling algorithm is proposed, and the model is validated through an extensive simulation study as well as an application to a biomedical dataset describing children's Body Mass Index and eating behavior.
