Towards Unifying Hamiltonian Monte Carlo and Slice Sampling

Part of Advances in Neural Information Processing Systems 29 (NIPS 2016)

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Authors

Yizhe Zhang, Xiangyu Wang, Changyou Chen, Ricardo Henao, Kai Fan, Lawrence Carin

Abstract

<p>We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS). We provide a theoretical analysis of the mixing performance of such samplers, proving that in the limit of a single parameter, the MGS draws decorrelated samples from the desired target distribution. We further show that as this parameter tends toward this limit, performance gains are achieved at a cost of increasing numerical difficulty and some practical convergence issues. Our theoretical results are validated with synthetic data and real-world applications.</p>