Coupling Nonparametric Mixtures via Latent Dirichlet Processes

Abstract

Mixture distributions are often used to model complex data. In this paper, we develop a new method that jointly estimates mixture models over multiple data sets by exploiting the statistical dependencies between them. Specifically, we introduce a set of latent Dirichlet processes as sources of component models (atoms), and for each data set, we construct a nonparametric mixture model by combining sub-sampled versions of the latent DPs. Each mixture model may acquire atoms from different latent DPs, while each atom may be shared by multiple mixtures. This multi-to-multi association distinguishes the proposed method from prior constructions that rely on tree or chain structures, allowing mixture models to be coupled more flexibly. In addition, we derive a sampling algorithm that jointly infers the model parameters and present experiments on both document analysis and image modeling.