A General Metric for Riemannian Manifold Hamiltonian Monte Carlo

TL;DR

This paper introduces a new Riemannian metric for Hamiltonian Monte Carlo that broadens its applicability to complex models, demonstrated through successful experiments on hierarchical and latent models.

Contribution

A novel metric for RMHMC that overcomes previous limitations, enabling its use on a wider range of models without requiring analytical convenience.

Findings

Successfully applied to hierarchical and latent models

Outperforms previous metrics in flexibility and applicability

Demonstrates effectiveness on complex distributions

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.