  Nonparametric mixture models based on the Dirichlet process are an elegant
alternative to finite models when the number of underlying components is
unknown, but inference in such models can be slow. Existing attempts to
parallelize inference in such models have relied on introducing approximations,
which can lead to inaccuracies in the posterior estimate. In this paper, we
describe auxiliary variable representations for the Dirichlet process and the
hierarchical Dirichlet process that allow us to sample from the true posterior
in a distributed manner. We show that our approach allows scalable inference
without the deterioration in estimate quality that accompanies existing
methods.
