ClusterCluster: Parallel Markov Chain Monte Carlo for Dirichlet Process Mixtures

TL;DR

This paper introduces a reparameterization of the Dirichlet process that enables parallel MCMC inference, significantly improving computational efficiency without altering the true posterior, demonstrated on large-scale data.

Contribution

The authors propose a novel reparameterization of the Dirichlet process that induces conditional independencies, allowing parallel MCMC inference without changing the posterior distribution.

Findings

Achieves efficient parallel inference on large datasets

Maintains the true posterior distribution during parallelization

Demonstrates scalability on data with over 1 million vectors

Abstract

The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian nonparametric modeling, and is widely used in tasks such as density estimation, natural language processing, and time series modeling. Although MCMC inference methods for the DP often provide a gold standard in terms asymptotic accuracy, they can be computationally expensive and are not obviously parallelizable. We propose a reparameterization of the Dirichlet process that induces conditional independencies between the atoms that form the random measure. This conditional independence enables many of the Markov chain transition operators for DP inference to be simulated in parallel across multiple cores. Applied to mixture modeling, our approach enables the Dirichlet process to simultaneously learn clusters that describe the data and superclusters that define the granularity of parallelization. Unlike previous approaches, our technique does not require alteration of the model and leaves the true posterior distribution invariant. It also naturally lends itself to a distributed software implementation in terms of Map-Reduce, which we test in cluster configurations of over 50 machines and 100 cores. We present experiments exploring the parallel efficiency and convergence properties of our approach on both synthetic and real-world data, including runs on 1MM data vectors in 256 dimensions.