Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo

TL;DR

This paper investigates how suboptimal cotangent disintegrations in Hamiltonian Monte Carlo affect its performance and introduces diagnostics to identify and address these issues for better application.

Contribution

It identifies the impact of cotangent disintegration choices on HMC performance and proposes diagnostics to detect suboptimal configurations.

Findings

Suboptimal cotangent disintegrations degrade HMC efficiency.

Diagnostics can reliably identify poor disintegration choices.

Proper tuning improves HMC scalability to high-dimensional problems.

Abstract

When properly tuned, Hamiltonian Monte Carlo scales to some of the most challenging high-dimensional problems at the frontiers of applied statistics, but when that tuning is suboptimal the performance leaves much to be desired. In this paper I show how suboptimal choices of one critical degree of freedom, the cotangent disintegration, manifest in readily observed diagnostics that facilitate the robust application of the algorithm.