Involutive MCMC: a Unifying Framework
Kirill Neklyudov, Max Welling, Evgenii Egorov, Dmitry Vetrov
Abstract
Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated, the way they are applied and how efficiently they sample. Despite all the differences, many of them share the same core principle, which we unify as the Involutive MCMC (iMCMC) framework. Building upon this, we describe a wide range of MCMC algorithms in terms of iMCMC, and formulate a number of “tricks” which one can use as design principles for developing new MCMC algorithms. Thus, iMCMC provides a unified view of many known MCMC algorithms, which facilitates the derivation of powerful extensions. We demonstrate the latter with two examples where we transform known reversible MCMC algorithms into more efficient irreversible ones.
BibTeX
@InProceedings{pmlr-v119-neklyudov20a,
title = {Involutive {MCMC}: a Unifying Framework},
author = {Neklyudov, Kirill and Welling, Max and Egorov, Evgenii and Vetrov, Dmitry},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {7273--7282},
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/neklyudov20a/neklyudov20a.pdf},
url = {https://proceedings.mlr.press/v119/neklyudov20a.html},
abstract = {Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated, the way they are applied and how efficiently they sample. Despite all the differences, many of them share the same core principle, which we unify as the Involutive MCMC (iMCMC) framework. Building upon this, we describe a wide range of MCMC algorithms in terms of iMCMC, and formulate a number of “tricks” which one can use as design principles for developing new MCMC algorithms. Thus, iMCMC provides a unified view of many known MCMC algorithms, which facilitates the derivation of powerful extensions. We demonstrate the latter with two examples where we transform known reversible MCMC algorithms into more efficient irreversible ones.}
}