Positive Curvature and Hamiltonian Monte Carlo
Abstract
The Jacobi metric introduced in mathematical physics can be used to analyze Hamiltonian Monte Carlo (HMC). In a geometrical setting, each step of HMC corresponds to a geodesic on a Riemannian manifold with a Jacobi metric. Our calculation of the sectional curvature of this HMC manifold allows us to see that it is positive in cases such as sampling from a high dimensional multivariate Gaussian. We show that positive curvature can be used to prove theoretical concentration results for HMC Markov chains.
Cite
Text
Seiler et al. "Positive Curvature and Hamiltonian Monte Carlo." Neural Information Processing Systems, 2014.Markdown
[Seiler et al. "Positive Curvature and Hamiltonian Monte Carlo." Neural Information Processing Systems, 2014.](https://mlanthology.org/neurips/2014/seiler2014neurips-positive/)BibTeX
@inproceedings{seiler2014neurips-positive,
title = {{Positive Curvature and Hamiltonian Monte Carlo}},
author = {Seiler, Christof and Rubinstein-Salzedo, Simon and Holmes, Susan},
booktitle = {Neural Information Processing Systems},
year = {2014},
pages = {586-594},
url = {https://mlanthology.org/neurips/2014/seiler2014neurips-positive/}
}