Fixed-Distance Hamiltonian Monte Carlo

Abstract

We propose a variation of the Hamiltonian Monte Carlo sampling (HMC) where the equations of motion are simulated for a fixed traversed distance rather than the conventional fixed simulation time. This new mechanism tends to generate proposals that have higher target probability values. The momentum distribution that is naturally joint with our Fixed-Distance HMC (FDHMC), and keeps the proposal acceptance probability close to 1, is not Gaussian and generates momentums that have a higher expected magnitude. This translates into a reduced correlation between the successive MCMC states and according to our experimental results, leads to an improvement in terms of the effective sample size per gradient when compared to the baseline HMC and No-U-Turn (NUTS) samplers.

PDF NeurIPS OpenReview Semantic Scholar

Cite

Text

Afshar and Cripps. "Fixed-Distance Hamiltonian Monte Carlo." Neural Information Processing Systems, 2022.

Markdown

[Afshar and Cripps. "Fixed-Distance Hamiltonian Monte Carlo." Neural Information Processing Systems, 2022.](https://mlanthology.org/neurips/2022/afshar2022neurips-fixeddistance/)

BibTeX

@inproceedings{afshar2022neurips-fixeddistance,
  title     = {{Fixed-Distance Hamiltonian Monte Carlo}},
  author    = {Afshar, Hadi Mohasel and Cripps, Sally},
  booktitle = {Neural Information Processing Systems},
  year      = {2022},
  url       = {https://mlanthology.org/neurips/2022/afshar2022neurips-fixeddistance/}
}