The Boomerang Sampler

J. Bierkens, S. Grazzi, K. Kamatani, G. O. Roberts

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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Abstract

This paper introduces the boomerang sampler as a novel class of continuous-time non-reversible Markov chain Monte Carlo algorithms. The methodology begins by representing the target density as a density, e(−U), with respect to a prescribed (usually) Gaussian measure and constructs a continuous trajectory consisting of a piecewise circular path. The method moves from one circular orbit to another according to a rate function which can be written in terms of U. We demonstrate that the method is easy to implement and demonstrate empirically that it can out-perform existing benchmark piecewise deterministic Markov processes such as the bouncy particle sampler and the Zig-Zag. In the Bayesian statistics context, these competitor algorithms are of substantial interest in the large data context due to the fact that they can adopt data subsampling techniques which are exact (ie induce no error in the stationary distribution). We demonstrate theoretically and empirically that we can also construct a control-variate subsampling boomerang sampler which is also exact, and which possesses remarkable scaling properties in the large data limit. We furthermore illustrate a factorised version on the simulation of diffusion bridges.
Original languageEnglish
Title of host publicationProceedings of the 37th International Conference on Machine Learning
Pages908-918
Number of pages11
Publication statusPublished - 2020
EventThe 37th International Conference on Machine Learning -
Duration: 12 Jul 202018 Jul 2020
Conference number: 37

Conference

ConferenceThe 37th International Conference on Machine Learning
Abbreviated titleICML
Period12/07/2018/07/20

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