Matrix-Variate Dirichlet Process Priors with Applications

Abstract

In this paper we propose a matrix-variate Dirichlet process (MATDP) for modeling the joint prior of a set of random matrices. Our approach is able to share statistical strength among regression coefficient matrices due to the clustering property of the Dirichlet process. Moreover, since the base probability measure is defined as a matrix-variate distribution, the dependence among the elements of each random matrix is described via the matrix-variate distribution. We apply MATDP to multivariate supervised learning problems. In particular, we devise a nonparametric discriminative model and a nonparametric latent factor model. The interest is in considering correlations both across response variables (or covariates) and across response vectors. We derive Markov chain Monte Carlo algorithms for posterior inference and prediction, and illustrate the application of the models to multivariate regression, multi-class classification and multi-label prediction problems.