Randomized Hamiltonian Monte Carlo
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Publication:1676436
DOI10.1214/16-AAP1255zbMATH Open1373.60129arXiv1511.09382OpenAlexW2185599544MaRDI QIDQ1676436
Author name not available (Why is that?)
Publication date: 7 November 2017
Published in: (Search for Journal in Brave)
Abstract: Tuning the durations of the Hamiltonian flow in Hamiltonian Monte Carlo (also called Hybrid Monte Carlo) (HMC) involves a tradeoff between computational cost and sampling quality, which is typically challenging to resolve in a satisfactory way. In this article we present and analyze a randomized HMC method (RHMC), in which these durations are i.i.d. exponential random variables whose mean is a free parameter. We focus on the small time step size limit, where the algorithm is rejection-free and the computational cost is proportional to the mean duration. In this limit, we prove that RHMC is geometrically ergodic under the same conditions that imply geometric ergodicity of the solution to underdamped Langevin equations. Moreover, in the context of a multi-dimensional Gaussian distribution, we prove that the sampling efficiency of RHMC, unlike that of constant duration HMC, behaves in a regular way. This regularity is also verified numerically in non-Gaussian target distributions. Finally we suggest variants of RHMC for which the time step size is not required to be small.
Full work available at URL: https://arxiv.org/abs/1511.09382
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