# Parallel Markov Chain Monte Carlo for the Indian Buffet Process

## TL;DR

This paper introduces a novel parallel MCMC algorithm for Indian Buffet Process models that achieves asymptotically exact inference by exploiting feature independence and combining collapsed and uncollapsed sampling.

## Contribution

It presents a hybrid parallel MCMC method that improves inference efficiency and accuracy for IBP models by partitioning features and collapsing the infinite tail.

## Key findings

- Achieves asymptotically exact posterior samples.
- Enables parallel inference without approximation.
- Improves mixing over previous methods.

## 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.