Although Hamiltonian Monte Carlo has proven an empirical success, the lack of
a rigorous theoretical understanding of the algorithm has in many ways impeded
both principled developments of the method and use of the algorithm in
practice. In this paper we develop the formal foundations of the algorithm
through the construction of measures on smooth manifolds, and demonstrate how
the theory naturally identifies efficient implementations and motivates
promising generalizations.
Description
[1410.5110] The Geometric Foundations of Hamiltonian Monte Carlo
%0 Journal Article
%1 betancourt2014geometric
%A Betancourt, M. J.
%A Byrne, Simon
%A Livingstone, Samuel
%A Girolami, Mark
%D 2014
%K bayesian geometry mcmc optimization probability readings stats
%T The Geometric Foundations of Hamiltonian Monte Carlo
%U http://arxiv.org/abs/1410.5110
%X Although Hamiltonian Monte Carlo has proven an empirical success, the lack of
a rigorous theoretical understanding of the algorithm has in many ways impeded
both principled developments of the method and use of the algorithm in
practice. In this paper we develop the formal foundations of the algorithm
through the construction of measures on smooth manifolds, and demonstrate how
the theory naturally identifies efficient implementations and motivates
promising generalizations.
@article{betancourt2014geometric,
abstract = {Although Hamiltonian Monte Carlo has proven an empirical success, the lack of
a rigorous theoretical understanding of the algorithm has in many ways impeded
both principled developments of the method and use of the algorithm in
practice. In this paper we develop the formal foundations of the algorithm
through the construction of measures on smooth manifolds, and demonstrate how
the theory naturally identifies efficient implementations and motivates
promising generalizations.},
added-at = {2019-07-20T20:31:39.000+0200},
author = {Betancourt, M. J. and Byrne, Simon and Livingstone, Samuel and Girolami, Mark},
biburl = {https://www.bibsonomy.org/bibtex/2ed91d642b6a39a6b3ce0772f01d7ce77/kirk86},
description = {[1410.5110] The Geometric Foundations of Hamiltonian Monte Carlo},
interhash = {0466c56da293b7610755b09942c15ee1},
intrahash = {ed91d642b6a39a6b3ce0772f01d7ce77},
keywords = {bayesian geometry mcmc optimization probability readings stats},
note = {cite arxiv:1410.5110Comment: 45 pages, 13 figures},
timestamp = {2020-02-20T22:09:38.000+0100},
title = {The Geometric Foundations of Hamiltonian Monte Carlo},
url = {http://arxiv.org/abs/1410.5110},
year = 2014
}