An Autoregressive Approach to Nonparametric Hierarchical Dependent Modeling

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Zhihua Zhang, Dakan Wang, Edward Chang ;
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:1416-1424, 2012.

Abstract

We propose a conditional autoregression framework for a collection of random probability measures. Under this framework, we devise a conditional autoregressive Dirichlet process (DP) that we call one-parameter dependent DP (wDDP). The appealing properties of this specification are that it has two equivalent representations and its inference can be implemented in a conditional Polya urn scheme. Moreover, these two representations bear a resemblance to the Polya urn scheme and the stick-breaking representation in the conventional DP. We apply this wDDP to Bayesian multivariate-response regression problems. An efficient Markov chain Monte Carlo algorithm is developed for Bayesian computation and prediction.

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