Improving sampling efficacy on high dimensional distributions with thin high density regions using Conservative Hamiltonian Monte Carlo

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ID: 315344
2026
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Abstract
Abstract Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics and generative models. However, such distributions tend to have thin high density regions, posing a significant challenge for symplectic integrators to maintain the small energy errors needed for a high acceptance probability. Instead, we propose a variant called Conservative Hamiltonian Monte Carlo, using R–reversible energy-preserving integrators to retain a high acceptance probability. We show our algorithm can achieve approximate stationarity with an error determined by the Jacobian approximation of the energy-preserving proposal map and its approximation error due to inexact solutions of implicit schemes. Numerical evidence shows improved convergence and robustness over integration parameters on target distributions with thin high density regions and in high dimensions. Moreover, a version of our algorithm can also be applied to target distributions without gradient information.
Reference Key
openalex_W7162853083 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Geoffrey McGregor, Andy T S Wan
Journal PNAS nexus
Year 2026
DOI
10.1093/pnasnexus/pgag178
URL
https://doi.org/10.1093/pnasnexus/pgag178
Keywords Keywords not found

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