2013/04/08 by Dan Lovell, D. A. Lovell, Jonathan Malmaud +6 · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Data Management and Algorithms #Distributed #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Parallel #and Cluster Computing (cs.DC) #cs.DC #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1304.2302
12 pages, 10 figures. Submitted to ICML 2013 during third submission cycle
arxiv created 2013/04/08 · openalex publication_date 2013/04/08 · arxiv updated 2013/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.