Identifying the Optimal Integration Time in Hamiltonian Monte Carlo

Abstract

By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided that the algorithm is sufficiently well-tuned. In this paper I show how the geometric foundations of Hamiltonian Monte Carlo implicitly identify the optimal choice of these parameters, especially the integration time. I then consider the practical consequences of these principles in both existing algorithms and a new implementation called \emph{Exhaustive Hamiltonian Monte Carlo} before demonstrating the utility of these ideas in some illustrative examples.

31 pages, 21 figures

References in corpus (1)

• Generalizing the No-U-Turn Sampler to Riemannian Manifolds

Cited by in corpus (7)

• On the Geometric Ergodicity of Hamiltonian Monte Carlo
• Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo
• Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters
• The Information Content of Projected Galaxy Fields
• Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents
• The TESS-Keck Survey. XIII. An Eccentric Hot Neptune with a Similar-Mass Outer Companion around TOI-1272
• Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations