Fast langevin based algorithm for MCMC in high dimensions

Alain Durmus; Gareth O. Roberts; Gilles Vilmart; Konstantinos C. Zygalakis

doi:10.1214/16-AAP1257

Fast langevin based algorithm for MCMC in high dimensions

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

CNRS LTCI
University of Warwick
University of Geneva
University of Edinburgh

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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(d^1/5) compared to the complexity 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.

langue originale	Anglais
Pages (de - à)	2195-2237
Nombre de pages	43
journal	Annals of Applied Probability
Volume	27
Numéro de publication	4
Les DOIs	https://doi.org/10.1214/16-AAP1257
état	Publié - 1 août 2017
Modification externe	Oui

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title = "Fast langevin based algorithm for MCMC in high dimensions",

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.",

keywords = "Diffusion limit, Exponential ergodicity, Markov chain Monte Carlo, Weak convergence",

author = "Alain Durmus and Roberts, \{Gareth O.\} and Gilles Vilmart and Zygalakis, \{Konstantinos C.\}",

note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2017.",

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doi = "10.1214/16-AAP1257",

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AU - Durmus, Alain

AU - Roberts, Gareth O.

AU - Vilmart, Gilles

AU - Zygalakis, Konstantinos C.

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2017.

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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.

KW - Diffusion limit

KW - Exponential ergodicity

KW - Markov chain Monte Carlo

KW - Weak convergence

UR - https://www.scopus.com/pages/publications/85028724242

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DO - 10.1214/16-AAP1257

M3 - Article

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SN - 1050-5164

VL - 27

SP - 2195

EP - 2237

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 4

ER -

Fast langevin based algorithm for MCMC in high dimensions

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