Skip to Main content Skip to Navigation
Reports

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

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.
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01919855
Contributor : Frederic Cazals <>
Submitted on : Monday, May 18, 2020 - 10:36:09 AM
Last modification on : Tuesday, May 19, 2020 - 1:43:54 AM

File

RR-9222-v2.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01919855, version 2

Collections

Citation

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⟩

Share

Metrics

Record views

31

Files downloads

14