Convergence of Preconditioned Hamiltonian Monte Carlo on Hilbert Spaces
Probability
2020-11-18 v1 Numerical Analysis
Numerical Analysis
Computation
Machine Learning
Abstract
In this article, we consider the preconditioned Hamiltonian Monte Carlo (pHMC) algorithm defined directly on an infinite-dimensional Hilbert space. In this context, and under a condition reminiscent of strong log-concavity of the target measure, we prove convergence bounds for adjusted pHMC in the standard 1-Wasserstein distance. The arguments rely on a synchronous coupling of two copies of pHMC, which is controlled by adapting elements from arXiv:1805.00452.
Keywords
Cite
@article{arxiv.2011.08578,
title = {Convergence of Preconditioned Hamiltonian Monte Carlo on Hilbert Spaces},
author = {Jakiw Pidstrigach},
journal= {arXiv preprint arXiv:2011.08578},
year = {2020}
}