Magnetic Hamiltonian Monte Carlo

Nilesh Tripuraneni, Mark Rowland, Zoubin Ghahramani, Richard Turner

ICML 2017 pp. 3453-3461

/icml/2017/tripuraneni2017icml-magnetic/

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 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.

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Text

Tripuraneni et al. "Magnetic Hamiltonian Monte Carlo." International Conference on Machine Learning, 2017.

Markdown

[Tripuraneni et al. "Magnetic Hamiltonian Monte Carlo." International Conference on Machine Learning, 2017.](https://mlanthology.org/icml/2017/tripuraneni2017icml-magnetic/)

BibTeX

@inproceedings{tripuraneni2017icml-magnetic,
  title     = {{Magnetic Hamiltonian Monte Carlo}},
  author    = {Tripuraneni, Nilesh and Rowland, Mark and Ghahramani, Zoubin and Turner, Richard},
  booktitle = {International Conference on Machine Learning},
  year      = {2017},
  pages     = {3453-3461},
  volume    = {70},
  url       = {https://mlanthology.org/icml/2017/tripuraneni2017icml-magnetic/}
}