  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.
