Matrix-Variate Dirichlet Process Mixture Models

We are concerned with a multivariate response regression problem where the interest is in considering correlations both across response variates and across response samples. In this paper we develop a new Bayesian nonparametric model for such a setting based on Dirichlet process priors. Building on an additive kernel model, we allow each sample to have its own regression matrix. Although this overcomplete representation could in principle suffer from severe overfitting problems, we are able to provide effective control over the model via a matrix-variate Dirichlet process prior on the regression matrices. Our model is able to share statistical strength among regression matrices due to the clustering property of the Dirichlet process. We make use of a Markov chain Monte Carlo algorithm for inference and prediction. Compared with other Bayesian kernel models, our model has advantages in both computational and statistical efficiency.