Poster
Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families
Heiko Strathmann · Dino Sejdinovic · Samuel Livingstone · Zoltan Szabo · Arthur Gretton

Wed Dec 9th 07:00 -- 11:59 PM @ 210 C #46 #None

We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities where classical HMC is not an option due to intractable gradients, KMC adaptively learns the target's gradient structure by fitting an exponential family model in a Reproducing Kernel Hilbert Space. Computational costs are reduced by two novel efficient approximations to this gradient. While being asymptotically exact, KMC mimics HMC in terms of sampling efficiency, and offers substantial mixing improvements over state-of-the-art gradient free samplers. We support our claims with experimental studies on both toy and real-world applications, including Approximate Bayesian Computation and exact-approximate MCMC.

Author Information

Heiko Strathmann (University College London)
Dino Sejdinovic (University of Oxford)
Samuel Livingstone (University College London)
Zoltan Szabo (Gatsby Unit, UCL)
Arthur Gretton (University Collage London)

Arthur Gretton is a Professor with the Gatsby Computational Neuroscience Unit at UCL. He received degrees in Physics and Systems Engineering from the Australian National University, and a PhD with Microsoft Research and the Signal Processing and Communications Laboratory at the University of Cambridge. He previously worked at the MPI for Biological Cybernetics, and at the Machine Learning Department, Carnegie Mellon University. Arthur's recent research interests in machine learning include the design and training of generative models, both implicit (e.g. GANs) and explicit (high/infinite dimensional exponential family models), nonparametric hypothesis testing, and kernel methods. He has been an associate editor at IEEE Transactions on Pattern Analysis and Machine Intelligence from 2009 to 2013, an Action Editor for JMLR since April 2013, an Area Chair for NeurIPS in 2008 and 2009, a Senior Area Chair for NeurIPS in 2018, an Area Chair for ICML in 2011 and 2012, and a member of the COLT Program Committee in 2013. Arthur was program chair for AISTATS in 2016 (with Christian Robert), tutorials chair for ICML 2018 (with Ruslan Salakhutdinov), workshops chair for ICML 2019 (with Honglak Lee), program chair for the Dali workshop in 2019 (with Krikamol Muandet and Shakir Mohammed), and co-organsier of the Machine Learning Summer School 2019 in London (with Marc Deisenroth).

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