Non-Volume Preserving Hamiltonian Monte Carlo and No-U-TurnSamplers

Hadi Mohasel Afshar, Rafael Oliveira, Sally Cripps
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1675-1683, 2021.

Abstract

Volume preservation is usually regarded as a necessary property for the leapfrog transition functions that are used in Hamiltonian Monte Carlo (HMC) and No-U-Turn (NUTS) samplers to guarantee convergence to the target distribution. In this work we rigorously prove that with minimal algorithmic modifications, both HMC and NUTS can be combined with transition functions that are not necessarily volume preserving. In light of these results, we propose a non-volume preserving transition function that conserves the Hamiltonian better than the baseline leapfrog mechanism, on piecewise-continuous distributions. The resulting samplers do not require any assumptions on the geometry of the discontinuity boundaries, and our experimental results show a significant improvement upon traditional HMC and NUTS.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-mohasel-afshar21a, title = { Non-Volume Preserving Hamiltonian Monte Carlo and No-U-TurnSamplers }, author = {Mohasel Afshar, Hadi and Oliveira, Rafael and Cripps, Sally}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1675--1683}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/mohasel-afshar21a/mohasel-afshar21a.pdf}, url = {https://proceedings.mlr.press/v130/mohasel-afshar21a.html}, abstract = { Volume preservation is usually regarded as a necessary property for the leapfrog transition functions that are used in Hamiltonian Monte Carlo (HMC) and No-U-Turn (NUTS) samplers to guarantee convergence to the target distribution. In this work we rigorously prove that with minimal algorithmic modifications, both HMC and NUTS can be combined with transition functions that are not necessarily volume preserving. In light of these results, we propose a non-volume preserving transition function that conserves the Hamiltonian better than the baseline leapfrog mechanism, on piecewise-continuous distributions. The resulting samplers do not require any assumptions on the geometry of the discontinuity boundaries, and our experimental results show a significant improvement upon traditional HMC and NUTS. } }
Endnote
%0 Conference Paper %T Non-Volume Preserving Hamiltonian Monte Carlo and No-U-TurnSamplers %A Hadi Mohasel Afshar %A Rafael Oliveira %A Sally Cripps %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-mohasel-afshar21a %I PMLR %P 1675--1683 %U https://proceedings.mlr.press/v130/mohasel-afshar21a.html %V 130 %X Volume preservation is usually regarded as a necessary property for the leapfrog transition functions that are used in Hamiltonian Monte Carlo (HMC) and No-U-Turn (NUTS) samplers to guarantee convergence to the target distribution. In this work we rigorously prove that with minimal algorithmic modifications, both HMC and NUTS can be combined with transition functions that are not necessarily volume preserving. In light of these results, we propose a non-volume preserving transition function that conserves the Hamiltonian better than the baseline leapfrog mechanism, on piecewise-continuous distributions. The resulting samplers do not require any assumptions on the geometry of the discontinuity boundaries, and our experimental results show a significant improvement upon traditional HMC and NUTS.
APA
Mohasel Afshar, H., Oliveira, R. & Cripps, S.. (2021). Non-Volume Preserving Hamiltonian Monte Carlo and No-U-TurnSamplers . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1675-1683 Available from https://proceedings.mlr.press/v130/mohasel-afshar21a.html.

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