Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families

TL;DR

Kernel Hamiltonian Monte Carlo (KMC) is a gradient-free adaptive MCMC method that learns target gradients intractable for classical HMC, offering efficient sampling and substantial mixing improvements over existing gradient-free methods.

Contribution

The paper introduces KMC, a novel gradient-free adaptive MCMC algorithm that learns target gradients via exponential family models in RKHS, reducing computational costs with new approximations.

Findings

KMC achieves asymptotic exactness and mimics HMC efficiency.

KMC demonstrates superior mixing over existing gradient-free samplers.

Experimental results include toy models and real-world applications like ABC.

Abstract

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.