CUED Publications database

Magnetic Hamiltonian Monte Carlo

Tripuraneni, N and Rowland, M and Ghahramani, Z and Turner, R Magnetic Hamiltonian Monte Carlo. (Unpublished)

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Abstract

Hamiltonian Monte Carlo (HMC) exploits Hamiltonian dynamics to construct efficient proposals for Markov chain Monte Carlo (MCMC). In this paper, we present a generalization of HMC which exploits \textit{non-canonical} Hamiltonian dynamics. We refer to this algorithm as magnetic HMC, since in 3 dimensions a subset of the dynamics map onto the mechanics of a charged particle coupled to a magnetic field. We establish a theoretical basis for the use of non-canonical Hamiltonian dynamics in MCMC, and construct a symplectic, leapfrog-like integrator allowing for the implementation of magnetic HMC. Finally, we exhibit several examples where these non-canonical dynamics can lead to improved mixing of magnetic HMC relative to ordinary HMC.

Item Type: Article
Uncontrolled Keywords: stat.ML stat.ML
Subjects: UNSPECIFIED
Divisions: Div F > Computational and Biological Learning
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 20:14
Last Modified: 29 Aug 2017 01:17
DOI: