  Bayesian nonparametric (BNP) models provide elegant methods for discovering
underlying latent features within a data set, but inference in such models can
be slow. We exploit the fact that completely random measures, which commonly
used models like the Dirichlet process and the beta-Bernoulli process can be
expressed as, are decomposable into independent sub-measures. We use this
decomposition to partition the latent measure into a finite measure containing
only instantiated components, and an infinite measure containing all other
components. We then select different inference algorithms for the two
components: uncollapsed samplers mix well on the finite measure, while
collapsed samplers mix well on the infinite, sparsely occupied tail. The
resulting hybrid algorithm can be applied to a wide class of models, and can be
easily distributed to allow scalable inference without sacrificing asymptotic
convergence guarantees.
