A Family of MCMC Methods on Implicitly Defined Manifolds
Abstract
Traditional MCMC methods are only applicable to distributions which can be defined on \mathbb{R}^n. However, there exist many application domains where the distributions cannot easily be defined on a Euclidean space. To address this limitation, we propose a general constrained version of Hamiltonian Monte Carlo, and give conditions under which the Markov chain is convergent. Based on this general framework we define a family of MCMC methods which can be applied to sample from distributions on non-linear manifolds. We demonstrate the effectiveness of our approach on a variety of problems including sampling from the Bingham-von Mises-Fisher distribution, collaborative filtering and human pose estimation.
Cite
Text
Brubaker et al. "A Family of MCMC Methods on Implicitly Defined Manifolds." Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, 2012.Markdown
[Brubaker et al. "A Family of MCMC Methods on Implicitly Defined Manifolds." Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, 2012.](https://mlanthology.org/aistats/2012/brubaker2012aistats-family/)BibTeX
@inproceedings{brubaker2012aistats-family,
title = {{A Family of MCMC Methods on Implicitly Defined Manifolds}},
author = {Brubaker, Marcus and Salzmann, Mathieu and Urtasun, Raquel},
booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics},
year = {2012},
pages = {161-172},
volume = {22},
url = {https://mlanthology.org/aistats/2012/brubaker2012aistats-family/}
}