The Boomerang Sampler

TL;DR

The Boomerang Sampler is a new continuous-time non-reversible MCMC method that constructs elliptical trajectories for efficient sampling, outperforming existing algorithms and scaling well with large data, especially with subsampling techniques.

Contribution

It introduces the Boomerang Sampler, a novel non-reversible MCMC algorithm with a new elliptical trajectory approach, and demonstrates its efficiency and scalability, including subsampling variants.

Findings

Outperforms existing piecewise deterministic Markov processes.

Can be combined with exact data subsampling techniques.

Exhibits remarkable scaling properties in large data settings.

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 elliptical path. The method moves from one elliptical 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.