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Hamiltonian Monte Carlo with boundary reflections, and application to polytope volume calculations

Augustin Chevallier 1 Sylvain Pion 2 Frédéric Cazals 1
1 ABS - Algorithms, Biology, Structure
CRISAM - Inria Sophia Antipolis - Méditerranée
2 AUCTUS - Augmenting human comfort in the factory using cobots
Inria Bordeaux - Sud-Ouest, Bordeaux INP - Institut Polytechnique de Bordeaux
Abstract : This paper studies HMC with reflections on the boundary of a domain, providing an enhanced alternative to Hit-and-run (HAR) to sample a target distribution in a bounded domain. We make three contributions. First, we provide a convergence bound, paving the way to more precise mixing time analysis. Second, we present a robust implementation based on multi-precision arithmetic – a mandatory ingredient to guarantee exact predicates and robust constructions. Third, we use our HMC random walk to perform polytope volume calculations, using it as an alternative to HAR within the volume algorithm by Cousins and Vempala. The tests, conducted up to dimension 50, show that the HMC RW outperforms HAR.
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https://hal.archives-ouvertes.fr/hal-01919855
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Submitted on : Monday, May 18, 2020 - 10:36:09 AM
Last modification on : Tuesday, February 9, 2021 - 4:14:06 PM

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  • HAL Id : hal-01919855, version 2

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Augustin Chevallier, Sylvain Pion, Frédéric Cazals. Hamiltonian Monte Carlo with boundary reflections, and application to polytope volume calculations. [Research Report] RR-9222, INRIA Sophia Antipolis, France. 2018. ⟨hal-01919855v2⟩

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