Magnetic Hamiltonian Monte Carlo

Nilesh Tripuraneni, Mark Rowland, Zoubin Ghahramani, Richard Turner
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3453-3461, 2017.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-tripuraneni17a, title = {Magnetic {H}amiltonian {M}onte {C}arlo}, author = {Nilesh Tripuraneni and Mark Rowland and Zoubin Ghahramani and Richard Turner}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {3453--3461}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/tripuraneni17a/tripuraneni17a.pdf}, url = {https://proceedings.mlr.press/v70/tripuraneni17a.html}, 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.} }
Endnote
%0 Conference Paper %T Magnetic Hamiltonian Monte Carlo %A Nilesh Tripuraneni %A Mark Rowland %A Zoubin Ghahramani %A Richard Turner %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-tripuraneni17a %I PMLR %P 3453--3461 %U https://proceedings.mlr.press/v70/tripuraneni17a.html %V 70 %X 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.
APA
Tripuraneni, N., Rowland, M., Ghahramani, Z. & Turner, R.. (2017). Magnetic Hamiltonian Monte Carlo. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:3453-3461 Available from https://proceedings.mlr.press/v70/tripuraneni17a.html.

Related Material