Stochastic Bouncy Particle Sampler

Ari Pakman, Dar Gilboa, David Carlson, Liam Paninski
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:2741-2750, 2017.

Abstract

We introduce a stochastic version of the non-reversible, rejection-free Bouncy Particle Sampler (BPS), a Markov process whose sample trajectories are piecewise linear, to efficiently sample Bayesian posteriors in big datasets. We prove that in the BPS no bias is introduced by noisy evaluations of the log-likelihood gradient. On the other hand, we argue that efficiency considerations favor a small, controllable bias, in exchange for faster mixing. We introduce a simple method that controls this trade-off. We illustrate these ideas in several examples which outperform previous approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-pakman17a, title = {Stochastic Bouncy Particle Sampler}, author = {Ari Pakman and Dar Gilboa and David Carlson and Liam Paninski}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {2741--2750}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/pakman17a/pakman17a.pdf}, url = {https://proceedings.mlr.press/v70/pakman17a.html}, abstract = {We introduce a stochastic version of the non-reversible, rejection-free Bouncy Particle Sampler (BPS), a Markov process whose sample trajectories are piecewise linear, to efficiently sample Bayesian posteriors in big datasets. We prove that in the BPS no bias is introduced by noisy evaluations of the log-likelihood gradient. On the other hand, we argue that efficiency considerations favor a small, controllable bias, in exchange for faster mixing. We introduce a simple method that controls this trade-off. We illustrate these ideas in several examples which outperform previous approaches.} }
Endnote
%0 Conference Paper %T Stochastic Bouncy Particle Sampler %A Ari Pakman %A Dar Gilboa %A David Carlson %A Liam Paninski %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-pakman17a %I PMLR %P 2741--2750 %U https://proceedings.mlr.press/v70/pakman17a.html %V 70 %X We introduce a stochastic version of the non-reversible, rejection-free Bouncy Particle Sampler (BPS), a Markov process whose sample trajectories are piecewise linear, to efficiently sample Bayesian posteriors in big datasets. We prove that in the BPS no bias is introduced by noisy evaluations of the log-likelihood gradient. On the other hand, we argue that efficiency considerations favor a small, controllable bias, in exchange for faster mixing. We introduce a simple method that controls this trade-off. We illustrate these ideas in several examples which outperform previous approaches.
APA
Pakman, A., Gilboa, D., Carlson, D. & Paninski, L.. (2017). Stochastic Bouncy Particle Sampler. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:2741-2750 Available from https://proceedings.mlr.press/v70/pakman17a.html.

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