Section: New Results
Hamiltonian Monte Carlo with boundary reflections, and application to polytope volume calculations
In this work , we studied 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.
This work is a collaboration with Frédéric Cazals and Augustin Chevallier from the ABS team at Inria Sophia-Antipolis. Augustin Chevallier visited our team on May 17-18, 2018. Volume calculation is a topic of interest for AUCTUS in light of the volume of configuration spaces.