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.

34th International Conference on Machine Learning (ICML 2017)

Cited by in corpus (8)

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• Generalizing Hamiltonian Monte Carlo with Neural Networks
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• Antithetic Riemannian Manifold And Quantum-Inspired Hamiltonian Monte Carlo
• Magnetic Manifold Hamiltonian Monte Carlo
• Variational Langevin Hamiltonian Monte Carlo for Distant Multi-modal Sampling