Bayesian nonparametric models on decomposable graphs

Over recent years Dirichlet processes and the associated Chinese restaurant process (CRP) have found many applications in clustering while the Indian buffet process (IBP) is increasingly used to describe latent feature models. These models are attractive because they ensure exchangeability (over samples). We propose here extensions of these models where the dependency between samples is given by a known decomposable graph. These models have appealing properties and can be easily learned using Monte Carlo techniques