  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 the random-walk proposals. However,
probabilistic inference involving multi-modal distributions is very difficult
for standard HMC method, especially when the modes are far away from each
other. Sampling algorithms are then often incapable of traveling across the
places of low probability. In this paper, we propose a novel MCMC algorithm
which aims to sample from multi-modal distributions effectively. The method
improves Hamiltonian dynamics to reduce the autocorrelation of the samples and
uses a variational distribution to explore the phase space and find new modes.
A formal proof is provided which 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.
