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Average of Recentered Parallel MCMC for Big Data

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1706.04780.pdf (268.3Kb)
Date
2017
Publisher city
Paris
Publishing date
2017
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Dewey
Traitement du signal
Sujet
MCMC; big data
URI
https://basepub.dauphine.fr/handle/123456789/18741
Collections
  • CEREMADE : Publications
Metadata
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Author
Robert, Christian P.
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Wu, Changye
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
14
Abstract (EN)
In big data context, traditional MCMC methods, such as Metropolis-Hastings algorithms and hybrid Monte Carlo, scale poorly because of their need to evaluate the likelihood over the whole data set at each iteration. In order to resurrect MCMC methods, numerous approaches belonging to two categories: divide-and-conquer and subsampling, are proposed. In this article, we study the parallel MCMC and propose a new combination method in the divide-and-conquer framework. Compared with some parallel MCMC methods, such as consensus Monte Carlo, Weierstrass Sampler, instead of sampling from subposteriors, our method runs MCMC on rescaled subposteriors, but share the same computation cost in the parallel stage. We also give the mathematical justification of our method and show its performance in several models. Besides, even though our new methods is proposed in parametric framework, it can been applied to non-parametric cases without difficulty.

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