Continuously tempered Hamiltonian Monte Carlo

Matthew M. Graham, Amos J. Storkey
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:211-220, 2017.

Abstract

Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) method for performing approximate inference in com- plex probabilistic models of continuous vari- ables. In common with many MCMC methods, however, the standard HMC approach performs poorly in distributions with multiple isolated modes. We present a method for augmenting the Hamiltonian system with an extra continu- ous temperature control variable which allows the dynamic to bridge between sampling a com- plex target distribution and a simpler unimodal base distribution. This augmentation both helps improve mixing in multimodal targets and al- lows the normalisation constant of the target distribution to be estimated. The method is sim- ple to implement within existing HMC code, re- quiring only a standard leapfrog integrator. We demonstrate experimentally that the method is competitive with annealed importance sampling and simulating tempering methods at sampling from challenging multimodal distributions and estimating their normalising constants.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-graham17a, title = {Continuously tempered {H}amiltonian {M}onte {C}arlo}, author = {Graham, Matthew M. and Storkey, Amos J.}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {211--220}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/graham17a/graham17a.pdf}, url = {https://proceedings.mlr.press/r15/graham17a.html}, abstract = {Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) method for performing approximate inference in com- plex probabilistic models of continuous vari- ables. In common with many MCMC methods, however, the standard HMC approach performs poorly in distributions with multiple isolated modes. We present a method for augmenting the Hamiltonian system with an extra continu- ous temperature control variable which allows the dynamic to bridge between sampling a com- plex target distribution and a simpler unimodal base distribution. This augmentation both helps improve mixing in multimodal targets and al- lows the normalisation constant of the target distribution to be estimated. The method is sim- ple to implement within existing HMC code, re- quiring only a standard leapfrog integrator. We demonstrate experimentally that the method is competitive with annealed importance sampling and simulating tempering methods at sampling from challenging multimodal distributions and estimating their normalising constants.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Continuously tempered Hamiltonian Monte Carlo %A Matthew M. Graham %A Amos J. Storkey %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-graham17a %I PMLR %P 211--220 %U https://proceedings.mlr.press/r15/graham17a.html %V R15 %X Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) method for performing approximate inference in com- plex probabilistic models of continuous vari- ables. In common with many MCMC methods, however, the standard HMC approach performs poorly in distributions with multiple isolated modes. We present a method for augmenting the Hamiltonian system with an extra continu- ous temperature control variable which allows the dynamic to bridge between sampling a com- plex target distribution and a simpler unimodal base distribution. This augmentation both helps improve mixing in multimodal targets and al- lows the normalisation constant of the target distribution to be estimated. The method is sim- ple to implement within existing HMC code, re- quiring only a standard leapfrog integrator. We demonstrate experimentally that the method is competitive with annealed importance sampling and simulating tempering methods at sampling from challenging multimodal distributions and estimating their normalising constants. %Z Reissued by PMLR on 04 October 2026.
APA
Graham, M.M. & Storkey, A.J.. (2017). Continuously tempered Hamiltonian Monte Carlo. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:211-220 Available from https://proceedings.mlr.press/r15/graham17a.html. Reissued by PMLR on 04 October 2026.

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