A0158
Title: Inverse bounds and posterior contraction of the latent mixing measures
Authors: Long Nguyen - University of Michigan (United States) [presenting]
Abstract: New results on the posterior contraction behaviour of latent mixing measures that arise in infinite and finite mixture models are presented. At the heart of this theory is a collection of inverse bounds inequalities which provide upper bounds of an optimal transport distance of mixing measures in terms of a distance of corresponding data population distributions. For infinite mixtures, existing posterior contraction results measured in terms of the Wasserstein metrics are quite rare and confined to location mixtures. Nonetheless, more can still be said for Gaussian mixtures in particular, where it can be shown that while the overall convergence behaviour is slow, the parameters in the outlier regions of the parameter space converge almost at polynomial rates. This is possible by employing a generalized notion of optimal transport distance known as the Orlicz-Wasserstein metric. This is a welcome result for the practitioners of (infinite) Gaussian mixtures who wish to be able to interpret the model parameters efficiently. For finite mixtures where the number of components is unknown, a rather general theory has emerged based on a novel notion of strong identifiability with respect to any class of test functions subject to suitable conditions. This theory allows us to analyze a broader class of mixtures than has been considered before.
