Parallel Gibbs Sampling for Hierarchical Dirichlet Processes via Gamma Processes Equivalence

The hierarchical Dirichlet process (HDP) is an intuitive and elegant technique to model data with latent groups. However, it has not been widely used for practical applications due to the high computational costs associated with inference. In this paper, we propose an effective parallel Gibbs sampling algorithm for HDP by exploring its connections with the gamma-gamma-Poisson process. Specifically, we develop a novel framework that combines bootstrap and Reversible Jump MCMC algorithm to enable parallel variable updates. We also provide theoretical convergence analysis based on Gibbs sampling with asynchronous variable updates. Experiment results on both synthetic datasets and two large-scale text collections show that our algorithm can achieve considerable speedup as well as better inference accuracy for HDP compared with existing parallel sampling algorithms.