Hamiltonian Monte Carlo (HMC) is a powerful approach to Markov Chain Monte Carlo, since it generates successive samples with low correlation even for distributions in high dimensions and with complex nonlinear support. For some target densities, however, HMC cannot be applied, since the likelihood and its gradients are not computable in closed form (for instance, in Gaussian process classification). On target densities where classical HMC is not an option, KMC adaptively learns the target's gradient structure by fitting an infinite dimensional exponential family model in a Reproducing Kernel Hilbert Space. Our talk addresses two topics: first, we describe the properties of the exponential family model, show consistency for a wide class of target densities, and provide convergence rates under smoothness assumptions. Second, we demonstrate two strategies to approximate the gradient of this model efficiently, and show how these approximate gradients may be used in constructing an adaptive Hamiltonian Monte Carlo sampler. We establish empirical performance of the kernel adaptive HMC sampler with experimental studies on both toy and real-world applications, including exact-approximate MCMC for Gaussian process classification.
Arthur Gretton is a Reader (Associate Professor) with the Gatsby Computational Neuroscience Unit, University College London. Arthur's research interests include machine learning, kernel methods, statistical learning theory, nonparametric hypothesis testing, nonparametric density estimation, and techniques for neural data analysis. He has been an Action Editor for JMLR since April 2013, an associate editor at IEEE Transactions on Pattern Analysis and Machine Intelligence from 2009 to 2013, a member of the NIPS Program Committee in 2008 and 2009, an Area Chair for ICML in 2011 and 2012, and a member of the COLT Program Committee in 2013. Arthur was co-chair of AISTATS in 2016. 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.