Stochastic approximation Hamiltonian Monte Carlo

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 is more efficient than HMC-based implementations.

Keywords:

• Hamiltonian Monte Carlo
• stochastic approximation Monte Carlo
• multimodality
• scalable computation
• neural networks

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Research Foundation of Korea [ NRF 2020R1A2C1A01009881] and Yonsei University Research Fund [2019-22-0210].