Magnetic Hamiltonian Monte Carlo
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.
Keywords
Cite
@article{arxiv.1607.02738,
title = {Magnetic Hamiltonian Monte Carlo},
author = {Nilesh Tripuraneni and Mark Rowland and Zoubin Ghahramani and Richard Turner},
journal= {arXiv preprint arXiv:1607.02738},
year = {2017}
}
Comments
34th International Conference on Machine Learning (ICML 2017)