Fast Langevin based algorithm for MCMC in high dimensions

Alain Durmus*, Gareth O. Roberts, Gilles Vilmart, Konstantinos C. Zygalakis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 O(d1/5) compared to the complexity O(d1/3) 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.
Original languageEnglish
Pages (from-to)2195-2237
Number of pages43
JournalAnnals of Applied Probability
Volume27
Issue number4
DOIs
Publication statusPublished - 31 Aug 2017

Keywords

  • Weak convergence
  • Markov chain Monte Carlo
  • diffusion limit
  • exponential ergodicity
  • METROPOLIS-HASTINGS ALGORITHMS
  • TRANSIENT PHASE
  • CONVERGENCE
  • APPROXIMATIONS
  • DIFFUSIONS
  • EQUATIONS

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