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.

    Authors

    Nilesh Tripuraneni, Mark Rowland, Zoubin Ghahramani, Richard Turner

    Conference

    ICML 2017

    Full Paper

    ‘Magnetic Hamiltonian Monte Carlo’ (PDF)

    Uber AI

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