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Nonreversible Langevin Samplers: Splitting Schemes, Analysis and Implementation

A. Duncan,G. Pavliotis,K. Zygalakis

Published 2017 in arXiv: Methodology

ABSTRACT

For a given target density, there exist an infinite number of diffusion processes which are ergodic with respect to this density. As observed in a number of papers, samplers based on nonreversible diffusion processes can significantly outperform their reversible counterparts both in terms of asymptotic variance and rate of convergence to equilibrium. In this paper, we take advantage of this in order to construct efficient sampling algorithms based on the Lie-Trotter decomposition of a nonreversible diffusion process into reversible and nonreversible components. We show that samplers based on this scheme can significantly outperform standard MCMC methods, at the cost of introducing some controlled bias. In particular, we prove that numerical integrators constructed according to this decomposition are geometrically ergodic and characterise fully their asymptotic bias and variance, showing that the sampler inherits the good mixing properties of the underlying nonreversible diffusion. This is illustrated further with a number of numerical examples ranging from highly correlated low dimensional distributions, to logistic regression problems in high dimensions as well as inference for spatial models with many latent variables.

PUBLICATION RECORD

  • Publication year

    2017

  • Venue

    arXiv: Methodology

  • Publication date

    2017-01-16

  • Fields of study

    Mathematics, Physics

  • Identifiers
    arXiv 1701.04247
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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