Hamiltonian Monte Carlo Swindles

Dan Piponi, Matthew Hoffman, Pavel Sountsov
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3774-3783, 2020.

Abstract

Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) algorithm for estimating expectations with respect to continuous un-normalized probability distributions. MCMC estimators typically have higher variance than classical Monte Carlo with i.i.d. samples due to autocorrelations; most MCMC research tries to reduce these autocorrelations. In this work, we explore a complementary approach to variance reduction based on two classical Monte Carlo ’swindles’: first, running an auxiliary coupled chain targeting a tractable approximation to the target distribution, and using the auxiliary samples as control variates; and second, generating anti-correlated ("antithetic") samples by running two chains with flipped randomness. Both ideas have been explored previously in the context of Gibbs samplers and random-walk Metropolis algorithms, but we argue that they are ripe for adaptation to HMC in light of recent coupling results from the HMC theory literature. For many posterior distributions, we find that these swindles generate effective sample sizes orders of magnitude larger than plain HMC, as well as being more efficient than analogous swindles for Metropolis-adjusted Langevin algorithm and random-walk Metropolis.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-piponi20a, title = {Hamiltonian Monte Carlo Swindles}, author = {Piponi, Dan and Hoffman, Matthew and Sountsov, Pavel}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {3774--3783}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/piponi20a/piponi20a.pdf}, url = {https://proceedings.mlr.press/v108/piponi20a.html}, abstract = {Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) algorithm for estimating expectations with respect to continuous un-normalized probability distributions. MCMC estimators typically have higher variance than classical Monte Carlo with i.i.d. samples due to autocorrelations; most MCMC research tries to reduce these autocorrelations. In this work, we explore a complementary approach to variance reduction based on two classical Monte Carlo ’swindles’: first, running an auxiliary coupled chain targeting a tractable approximation to the target distribution, and using the auxiliary samples as control variates; and second, generating anti-correlated ("antithetic") samples by running two chains with flipped randomness. Both ideas have been explored previously in the context of Gibbs samplers and random-walk Metropolis algorithms, but we argue that they are ripe for adaptation to HMC in light of recent coupling results from the HMC theory literature. For many posterior distributions, we find that these swindles generate effective sample sizes orders of magnitude larger than plain HMC, as well as being more efficient than analogous swindles for Metropolis-adjusted Langevin algorithm and random-walk Metropolis. } }
Endnote
%0 Conference Paper %T Hamiltonian Monte Carlo Swindles %A Dan Piponi %A Matthew Hoffman %A Pavel Sountsov %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-piponi20a %I PMLR %P 3774--3783 %U https://proceedings.mlr.press/v108/piponi20a.html %V 108 %X Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) algorithm for estimating expectations with respect to continuous un-normalized probability distributions. MCMC estimators typically have higher variance than classical Monte Carlo with i.i.d. samples due to autocorrelations; most MCMC research tries to reduce these autocorrelations. In this work, we explore a complementary approach to variance reduction based on two classical Monte Carlo ’swindles’: first, running an auxiliary coupled chain targeting a tractable approximation to the target distribution, and using the auxiliary samples as control variates; and second, generating anti-correlated ("antithetic") samples by running two chains with flipped randomness. Both ideas have been explored previously in the context of Gibbs samplers and random-walk Metropolis algorithms, but we argue that they are ripe for adaptation to HMC in light of recent coupling results from the HMC theory literature. For many posterior distributions, we find that these swindles generate effective sample sizes orders of magnitude larger than plain HMC, as well as being more efficient than analogous swindles for Metropolis-adjusted Langevin algorithm and random-walk Metropolis.
APA
Piponi, D., Hoffman, M. & Sountsov, P.. (2020). Hamiltonian Monte Carlo Swindles. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:3774-3783 Available from https://proceedings.mlr.press/v108/piponi20a.html.

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