A0901
Title: On excess mass behavior in Gaussian mixture models with Orlicz-Wasserstein distances
Authors: Nhat Pham Minh Ho - University of Texas, Austin (United States) [presenting]
Abstract: Dirichlet process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. The aim is to (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. It is shown that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. The theoretical results provide new insight into understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, an algorithm to compute the metric is provided by leveraging Sinkhorn divergences, and findings are validated through a simulation study.
