Talk
Magnetic Hamiltonian Monte Carlo
Nilesh Tripuraneni · Mark Rowland · Zoubin Ghahramani · Richard E Turner

Wed Aug 9th 01:30 -- 01:48 PM @ C4.9& C4.10

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.

Author Information

Nilesh Tripuraneni (UC Berkeley)
Mark Rowland (University of Cambridge)
Zoubin Ghahramani (University of Cambridge & Uber)

Zoubin Ghahramani is a Professor at the University of Cambridge, and Chief Scientist at Uber. He is also Deputy Director of the Leverhulme Centre for the Future of Intelligence, was a founding Director of the Alan Turing Institute and co-founder of Geometric Intelligence (now Uber AI Labs). His research focuses on probabilistic approaches to machine learning and AI. In 2015 he was elected a Fellow of the Royal Society.

Richard E Turner (University of Cambridge)

Richard Turner holds a Lectureship (equivalent to US Assistant Professor) in Computer Vision and Machine Learning in the Computational and Biological Learning Lab, Department of Engineering, University of Cambridge, UK. He is a Fellow of Christ's College Cambridge. Previously, he held an EPSRC Postdoctoral research fellowship which he spent at both the University of Cambridge and the Laboratory for Computational Vision, NYU, USA. He has a PhD degree in Computational Neuroscience and Machine Learning from the Gatsby Computational Neuroscience Unit, UCL, UK and a M.Sci. degree in Natural Sciences (specialism Physics) from the University of Cambridge, UK. His research interests include machine learning, signal processing and developing probabilistic models of perception.

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