Stochastic dynamics without detailed balance condition connecting simple gradient method and Hamiltonian Monte Carlo

TL;DR

This paper unifies Hamiltonian Monte Carlo and non-detailed balance methods within a generalized framework, revealing their connection and proposing an efficient new Monte Carlo sampling technique.

Contribution

It provides a unified understanding of HMC and non-detailed balance approaches and introduces a novel, efficient Monte Carlo method based on this framework.

Findings

Unified HMC and non-detailed balance approaches

Proposed an efficient Monte Carlo sampling method

Enhanced understanding of sampling dynamics

Abstract

Sampling occupies an important position in theories of various scientific fields, and Markov chain Monte Carlo (MCMC) provides the most common technique of sampling. In the progress of MCMC, a huge number of studies have aimed the acceleration of convergence to the target distribution. Hamiltonian Monte Carlo (HMC) is such a variant of MCMC. In the recent development of MCMC, another approach based on the violation of the detailed balance condition has attracted much attention. Historically, these two approaches have been proposed independently, and their relationship has not been clearly understood. In this paper, the two approaches are seamlessly understood in the framework of generalized Monte Carlo method that violates the detailed balance condition. Furthermore we propose an efficient Monte Carlo method based on our framework.