Variational Hybrid Monte Carlo for Efficient Multi-Modal Data Sampling

Author:

Sun Shiliang1,Zhao Jing1ORCID,Gu Minghao1,Wang Shanhu1

Affiliation:

1. School of Computer Science and Technology, East China Normal University, Shanghai 200062, China

Abstract

The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient information of the target distribution, it can explore the state space much more efficiently than random-walk proposals, but may suffer from high autocorrelation. In this paper, we propose Langevin Hamiltonian Monte Carlo (LHMC) to reduce the autocorrelation of the samples. Probabilistic inference involving multi-modal distributions is very difficult for dynamics-based MCMC samplers, which is easily trapped in the mode far away from other modes. To tackle this issue, we further propose a variational hybrid Monte Carlo (VHMC) which uses a variational distribution to explore the phase space and find new modes, and it is capable of sampling from multi-modal distributions effectively. A formal proof is provided that shows that the proposed method can converge to target distributions. Both synthetic and real datasets are used to evaluate its properties and performance. The experimental results verify the theory and show superior performance in multi-modal sampling.

Funder

Shanghai Municipal Project under Grant

National Natural Science Foundation of China

Publisher

MDPI AG

Subject

General Physics and Astronomy

Reference38 articles.

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