Magnetic Hamiltonian Monte Carlo
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:34533461, 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 noncanonical 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 noncanonical Hamiltonian dynamics in MCMC, and construct a symplectic, leapfroglike integrator allowing for the implementation of magnetic HMC. Finally, we exhibit several examples where these noncanonical dynamics can lead to improved mixing of magnetic HMC relative to ordinary HMC.
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