GPU-accelerated Gibbs sampling: a case study of the Horseshoe Probit model
| Autor: | Shawfeng Dong, Alexander Terenin, David Draper |
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| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences Computer science Graphics processing unit 010103 numerical & computational mathematics Latent variable Statistics - Computation 01 natural sciences Theoretical Computer Science 010104 statistics & probability symbols.namesake Probit model 0101 mathematics Computation (stat.CO) Mathematical sciences Markov chain Monte Carlo Statistics::Computation Bayesian statistics Data point ComputingMethodologies_PATTERNRECOGNITION Computer Science - Distributed Parallel and Cluster Computing Computational Theory and Mathematics symbols Distributed Parallel and Cluster Computing (cs.DC) Statistics Probability and Uncertainty Algorithm Gibbs sampling |
| DOI: | 10.48550/arxiv.1608.04329 |
| Popis: | Gibbs sampling is a widely used Markov chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. Many implementations of MCMC methods do not extend easily to parallel computing environments, as their inherently sequential nature incurs a large synchronization cost. In the case study illustrated by this paper, we show how to do Gibbs sampling in a fully data-parallel manner on a graphics processing unit, for a large class of exchangeable models that admit latent variable representations. Our approach takes a systems perspective, with emphasis placed on efficient use of compute hardware. We demonstrate our method on a Horseshoe Probit regression model and find that our implementation scales effectively to thousands of predictors and millions of data points simultaneously. |
| Databáze: | OpenAIRE |
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