Mean field inference for the Dirichlet process mixture model

Abstract

We present a systematic study of several recently proposed methods of mean field inference for the Dirichlet process mixture (DPM) model. These methods provide approximations to the posterior distribution and are derived using the truncated stick-breaking representation and related approaches. We investigate their use in density estimation and cluster allocation and compare to Monte-Carlo results. Further, more specific topics include the general mathematical structure of the mean field approximation, the handling of the truncation level, the effect of including a prior on the concentration parameter α of the DPM model, the relationship between the proposed variants of the mean field approximation, and the connection to maximum a-posteriori estimation of the DPM model.