Abstract
By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided that the algorithm is sufficiently well-tuned. In this paper I show how the geometric foundations of Hamiltonian Monte Carlo implicitly identify the optimal choice of these parameters, especially the integration time. I then consider the practical consequences of these principles in both existing algorithms and a new implementation called \emph{Exhaustive Hamiltonian Monte Carlo} before demonstrating the utility of these ideas in some illustrative examples.
Keywords
Hybrid Monte CarloMarkov chain Monte CarloMonte Carlo methodMonte Carlo integrationMonte Carlo molecular modelingQuasi-Monte Carlo methodProbabilistic logicMonte Carlo method in statistical physicsHamiltonian (control theory)Computer scienceMathematical optimizationDynamic Monte Carlo methodStatistical physicsQuantum Monte CarloHamiltonian systemAlgorithmApplied mathematicsMathematicsPhysicsArtificial intelligenceMathematical analysisStatistics
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Publication Info
- Year
- 2016
- Type
- preprint
- Citations
- 30
- Access
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Cite This
Michael Betancourt
(2016).
Identifying the Optimal Integration Time in Hamiltonian Monte Carlo.
arXiv (Cornell University)
.
https://doi.org/10.48550/arxiv.1601.00225
Identifiers
- DOI
- 10.48550/arxiv.1601.00225