Preconditioned Discrete-HAMS: A Second-order Irreversible Discrete Sampler

TL;DR

This paper introduces the Preconditioned Discrete-HAMS (PDHAMS), a novel second-order irreversible sampler for discrete distributions that improves sampling efficiency by leveraging quadratic approximations and avoiding rejection.

Contribution

The paper develops PDHAMS, extending DHAMS with second-order approximations and Gaussian tricks, enabling rejection-free, irreversible sampling for quadratic potentials.

Findings

PDHAMS outperforms existing methods in numerical experiments.

The algorithm achieves rejection-free sampling for quadratic potentials.

It satisfies generalized detailed balance, enabling irreversible sampling.

Abstract

Gradient-based Markov Chain Monte Carlo methods have recently received much attention for sampling discrete distributions, with notable examples such as Norm Constrained Gradient (NCG), Auxiliary Variable Gradient (AVG), and Discrete Hamiltonian Assisted Metropolis Sampling (DHAMS). In this work, we propose the Preconditioned Discrete-HAMS (PDHAMS) algorithm, which extends DHAMS by incorporating a second-order, quadratic approximation of the potential function, and uses Gaussian integral trick to avoid directly sampling a pairwise Markov random field. The PDHAMS sampler not only satisfies generalized detailed balance, hence enabling irreversible sampling, but also is a rejection-free property for a target distribution with a quadratic potential function. In various numerical experiments, PDHAMS algorithms consistently yield superior performance compared with other methods.