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Unbiased Hamiltonian Monte Carlo with couplings

Author

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  • J Heng
  • P E Jacob

Abstract

SummaryWe propose a method for parallelization of Hamiltonian Monte Carlo estimators. Our approach involves constructing a pair of Hamiltonian Monte Carlo chains that are coupled in such a way that they meet exactly after some random number of iterations. These chains can then be combined so that the resulting estimators are unbiased. This allows us to produce independent replicates in parallel and average them to obtain estimators that are consistent in the limit of the number of replicates, rather than in the usual limit of the number of Markov chain iterations. We investigate the scalability of our coupling in high dimensions on a toy example. The choice of algorithmic parameters and the efficiency of our proposed approach are then illustrated on a logistic regression with 300 covariates and a log-Gaussian Cox point processes model with low- to fine-grained discretizations.

Suggested Citation

  • J Heng & P E Jacob, 2019. "Unbiased Hamiltonian Monte Carlo with couplings," Biometrika, Biometrika Trust, vol. 106(2), pages 287-302.
    • Handle: RePEc:oup:biomet:v:106:y:2019:i:2:p:287-302.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy074
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    Citations

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    Cited by:

    1. Zhengqing Zhou & Guanyang Wang & Jose Blanchet & Peter W. Glynn, 2021. "Unbiased Optimal Stopping via the MUSE," Papers 2106.02263, arXiv.org, revised Dec 2022.
    2. Pierre E. Jacob & John O’Leary & Yves F. Atchadé, 2020. "Unbiased Markov chain Monte Carlo methods with couplings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 543-600, July.
    3. Zhou, Zhengqing & Wang, Guanyang & Blanchet, Jose H. & Glynn, Peter W., 2023. "Unbiased Optimal Stopping via the MUSE," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    4. Liao, Kaihua & Lv, Ligang & Lai, Xiaoming & Zhu, Qing, 2021. "Toward a framework for the multimodel ensemble prediction of soil nitrogen losses," Ecological Modelling, Elsevier, vol. 456(C).

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