Article Dans Une Revue The Annals of Applied Probability Année : 2017

Fast Langevin based algorithm for MCMC in high dimensions

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(d1/5) compared to the complexity O(d1/3)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.

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A comme partie hal-01174226 Preprint Alain Durmus, Roberts O. Gareth, Gilles Vilmart, Konstantinos Zygalakis. Fast Langevin based algorithm for MCMC in high dimensions. 2015. ⟨hal-01174226⟩

Dates et versions

hal-01745692 , version 1 (03-09-2024)

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Alain Durmus, Gareth Roberts, Gilles Vilmart, Konstantinos Zygalakis. Fast Langevin based algorithm for MCMC in high dimensions. The Annals of Applied Probability, 2017, 27 (4), pp.2195 - 2237. ⟨10.1214/16-AAP1257⟩. ⟨hal-01745692⟩
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