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Peer-reviewedCC BYStatistics and Computing

Faster Hamiltonian Monte Carlo by learning leapfrog scale: an offline randomized solution

  • Changye Wu1
  • Pierre Pudlo2,3
  • Christian P. Robert1,4,3,5,6
  • Julien Stoehr1,7
7 affiliations
  1. 1CEREMADE, Université Paris-Dauphine, Université PSL, CNRS, 75016 Paris, France
  2. 2I2M, Aix Marseille Université, CNRS, 13003 Marseille, France
  3. 3CEntre de REcherches en MAthématiques de la DEcision
  4. 4Department of Statistics, University of Warwick, Coventry, CV4 7AL UK
  5. 5Centre de Recherche en Economie et en Statistique
  6. 6University of Warwick [Coventry]
  7. 7UMR MIA Paris-Saclay, Université Paris-Saclay, INRAE, AgroParisTech, 91120 Palaiseau, France
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Abstract

stands for empirical, leverages importance sampling to construct an empirical distribution on discretization parameters, thereby eliminating the need for manual burn-in diagnostics and online adaptation. The proposal distribution used in the calibration stage is obtained via a Population Monte Carlo scheme with tempering and relies on flexible parametric variational families such as normalizing flows. Once the calibration stage complete, the resulting algorithm defines a homogeneous Markov chain via a mixture of HMC kernels with a fixed mixing distribution, and hence preserves the target distribution. Numerical experiments indicate that eHMC can achieve competitive or improved sampling efficiency compared to the No-U-Turn Sampler (NUTS) in the case useful integration times can be summarized by the offline distribution. The comparison is assessed by standard efficiency metrics normalized by the number of leapfrog steps during the post-calibration sampling phase.

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Cite

BibTeXRIS
BibTeX
@article{wu2026faster,
  title = {{Faster Hamiltonian Monte Carlo by learning leapfrog scale: an offline randomized solution}},
  author = {Changye Wu and Pierre Pudlo and Christian P. Robert and Julien Stoehr},
  journal = {Statistics and Computing},
  year = {2026},
  month = sep,
  doi = {10.1007/s11222-026-10972-z},
  url = {https://doi.org/10.1007/s11222-026-10972-z},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Faster Hamiltonian Monte Carlo by learning leapfrog scale: an offline randomized solution
AU  - Changye Wu
AU  - Pierre Pudlo
AU  - Christian P. Robert
AU  - Julien Stoehr
PY  - 2026
DA  - 2026/09/23
JO  - Statistics and Computing
DO  - 10.1007/s11222-026-10972-z
UR  - https://doi.org/10.1007/s11222-026-10972-z
AB  - stands for empirical, leverages importance sampling to construct an empirical distribution on discretization parameters, thereby eliminating the need for manual burn-in diagnostics and online adaptation. The proposal distribution used in the calibration stage is obtained via a Population Monte Carlo scheme with tempering and relies on flexible parametric variational families such as normalizing flows. Once the calibration stage complete, the resulting algorithm defines a homogeneous Markov chain via a mixture of HMC kernels with a fixed mixing distribution, and hence preserves the target distribution. Numerical experiments indicate that eHMC can achieve competitive or improved sampling efficiency compared to the No-U-Turn Sampler (NUTS) in the case useful integration times can be summarized by the offline distribution. The comparison is assessed by standard efficiency metrics normalized by the number of leapfrog steps during the post-calibration sampling phase.
SN  - 0960-3174
SN  - 1573-1375
ER  -