Towards unifying hamiltonian Monte Carlo and Slice sampling

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

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.
Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems
PublisherNeural information processing systems foundation
Pages1749-1757
Number of pages9
StatePublished - Jan 1 2016
Externally publishedYes

Fingerprint Dive into the research topics of 'Towards unifying hamiltonian Monte Carlo and Slice sampling'. Together they form a unique fingerprint.

Cite this