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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    Zoubin Ghahramani
    Zoubin Ghahramani is Chief Scientist of Uber and a world leader in the field of machine learning, significantly advancing the state-of-the-art in algorithms that can learn from data. He is known in particular for fundamental contributions to probabilistic modeling and Bayesian approaches to machine learning systems and AI. Zoubin also maintains his roles as Professor of Information Engineering at the University of Cambridge and Deputy Director of the Leverhulme Centre for the Future of Intelligence. He was one of the founding directors of the Alan Turing Institute (the UK's national institute for Data Science and AI), and is a Fellow of St John's College Cambridge and of the Royal Society.