The Boomerang Sampler

Joris Bierkens, Sebastiano Grazzi, Kengo Kamatani, Gareth Roberts
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:908-918, 2020.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-bierkens20a, title = {The Boomerang Sampler}, author = {Bierkens, Joris and Grazzi, Sebastiano and Kamatani, Kengo and Roberts, Gareth}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {908--918}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/bierkens20a/bierkens20a.pdf}, url = {https://proceedings.mlr.press/v119/bierkens20a.html}, 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.} }
Endnote
%0 Conference Paper %T The Boomerang Sampler %A Joris Bierkens %A Sebastiano Grazzi %A Kengo Kamatani %A Gareth Roberts %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-bierkens20a %I PMLR %P 908--918 %U https://proceedings.mlr.press/v119/bierkens20a.html %V 119 %X 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.
APA
Bierkens, J., Grazzi, S., Kamatani, K. & Roberts, G.. (2020). The Boomerang Sampler. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:908-918 Available from https://proceedings.mlr.press/v119/bierkens20a.html.

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