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Paper · 1709.00404 · 2017

Unbiased Hamiltonian Monte Carlo with couplings

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 4 functions out of this paper's own repositories and ran 3 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
copy not recorded — 3 of 4
FunctionStatusWhere it lives
maximal_coupling Ran this paper's copy was not recorded; identical code first harvested from ColCarroll/couplings
pointer only · get_code("36d801042d0cb566")
maximal_coupling_reference Ran this paper's copy was not recorded; identical code first harvested from ColCarroll/couplings
pointer only · get_code("cf2b5d2f46ed1f2a")
unbiased_estimator Ran this paper's copy was not recorded; identical code first harvested from ColCarroll/couplings
pointer only · get_code("b42c95e02f86921f")
reflection_maximal_coupling Not yet run this paper's copy was not recorded; identical code first harvested from ColCarroll/couplings
pointer only · get_code("5102681d4097aefa")

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Abstract

We propose a methodology to parallelize Hamiltonian Monte Carlo estimators. Our approach constructs 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 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, instead of 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 methodology are then illustrated on a logistic regression with 300 covariates, and a log-Gaussian Cox point processes model with low to fine grained discretizations.

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