A General Metric for Riemannian Manifold Hamiltonian Monte Carlo

Abstract: Markov Chain Monte Carlo (MCMC) is an invaluable means of inference with complicated models, and Hamiltonian Monte Carlo, in particular Riemannian Manifold Hamiltonian Monte Carlo (RMHMC), has demonstrated impressive success in many challenging problems. Current RMHMC implementations, however, rely on a Riemannian metric that limits their application to analytically-convenient models. In this paper I propose a new metric for RMHMC without these limitations and verify its success on a distribution that emulates many hierarchical and latent models.