The Boomerang Sampler
This work addresses the problem of scalable Bayesian computation for statisticians and machine learning practitioners, offering an incremental improvement over existing piecewise deterministic Markov processes.
The paper tackles the challenge of designing efficient Markov chain Monte Carlo algorithms for large-scale Bayesian inference by introducing the Boomerang Sampler, a non-reversible continuous-time method that outperforms existing benchmarks like the bouncy particle sampler and Zig-Zag, with empirical demonstrations of superior performance and theoretical support for exact data subsampling.
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.