Unbiased Hamiltonian Monte Carlo with couplings

Summary We 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 t...

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Bibliographic Details
Published in:Biometrika 2019-06, Vol.106 (2), p.287-302
Main Authors: Heng, J, Jacob, P E
Format: Article
Language:English
Subjects:
Computer simulation
Couplings
Estimators
Gaussian process
Markov chains
Parallel processing
Random numbers
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Summary:Summary We 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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asy074