Title: Parallel Markov Chain Monte Carlo for the Indian Buffet Process,
Abstract: Indian Buffet Process based models are an elegant way for discovering
underlying features within a data set, but inference in such models can be
slow. Inferring underlying features using Markov chain Monte Carlo either
relies on an uncollapsed representation, which leads to poor mixing, or on a
collapsed representation, which leads to a quadratic increase in computational
complexity. Existing attempts at distributing inference have introduced
additional approximation within the inference procedure. In this paper we
present a novel algorithm to perform asymptotically exact parallel Markov chain
Monte Carlo inference for Indian Buffet Process models. We take advantage of
the fact that the features are conditionally independent under the
beta-Bernoulli process. Because of this conditional independence, we can
partition the features into two parts: one part containing only the finitely
many instantiated features and the other part containing the infinite tail of
uninstantiated features. For the finite partition, parallel inference is simple
given the instantiation of features. But for the infinite tail, performing
uncollapsed MCMC leads to poor mixing and hence we collapse out the features.
The resulting hybrid sampler, while being parallel, produces samples
asymptotically from the true posterior.