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Scientific article
Open access
English

Fast Langevin based algorithm for MCMC in high dimensions

Published inAnnals of Applied Probability, vol. 27, no. 4, p. 2195-2237
Publication date2017
Abstract

We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension $d$. The improved complexity is $mathcal{O}(d^{1/5})$ compared to the complexity $mathcal{O}(d^{1/3})$ of the standard approach. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate (with asymptotical value 0.704), independently of the target distribution. Numerical experiments confirm our theoretical findings.

Classification
  • arxiv : math.NA
Research group
Citation (ISO format)
DURMUS, Alain et al. Fast Langevin based algorithm for MCMC in high dimensions. In: Annals of Applied Probability, 2017, vol. 27, n° 4, p. 2195–2237. doi: 10.1214/16-AAP1257
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ISSN of the journal1050-5164
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Technical informations

Creation09/20/2017 9:06:00 AM
First validation09/20/2017 9:06:00 AM
Update time03/15/2023 2:02:50 AM
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