Stochastic Approximation Hamiltonian Monte Carlo

TL;DR

This paper introduces SAHMC, a novel stochastic approximation method that enhances Hamiltonian Monte Carlo's ability to sample efficiently from multimodal distributions by adaptively lowering energy barriers.

Contribution

SAHMC is a new algorithm that improves HMC's performance in multimodal distributions by adaptively reducing energy barriers to facilitate mode crossing.

Findings

SAHMC explores multimodal distributions more efficiently than traditional HMC.

SAHMC adaptively lowers energy barriers to improve sampling.

Simulation results demonstrate SAHMC's superior performance in multimodal settings.

Abstract

Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain cannot cross energy barrier between modes due to the energy conservation property. In this paper, we propose a Stochastic Approximate Hamilton Monte Carlo (SAHMC) algorithm for generating samples from multimodal density under the Hamiltonian Monte Carlo (HMC) framework. SAHMC can adaptively lower the energy barrier to move the Hamiltonian trajectory more frequently and more easily between modes. Our simulation studies show that the potential for SAHMC to explore a multimodal target distribution more efficiently than HMC based implementations.