Geometric No-U-Turn Samplers: Concepts and Evaluation
Abstract
We enhance geometric Markov Chain Monte Carlo methods, in particular making them easier to use by providing better tools for choosing the metric and various tuning parameters. We extend the No-U-Turn criterion for automatic choice of integration length for Lagrangian Monte Carlo and propose a modification to the computationally efficient Monge metric, as well as summarizing several previously proposed metric choices. Through extensive experimentation, including synthetic examples and posteriordb benchmarks, we demonstrate that Riemannian metrics can outperform Euclidean counterparts, particularly in scenarios with high curvature, while highlighting how the optimal choice of metric is problem-specific.
Cite
Text
Williams et al. "Geometric No-U-Turn Samplers: Concepts and Evaluation." Proceedings of The 12th International Conference on Probabilistic Graphical Models, 2024.Markdown
[Williams et al. "Geometric No-U-Turn Samplers: Concepts and Evaluation." Proceedings of The 12th International Conference on Probabilistic Graphical Models, 2024.](https://mlanthology.org/pgm/2024/williams2024pgm-geometric/)BibTeX
@inproceedings{williams2024pgm-geometric,
title = {{Geometric No-U-Turn Samplers: Concepts and Evaluation}},
author = {Williams, Bernardo and Yu, Hanlin and Hartmann, Marcelo and Klami, Arto},
booktitle = {Proceedings of The 12th International Conference on Probabilistic Graphical Models},
year = {2024},
pages = {327-347},
volume = {246},
url = {https://mlanthology.org/pgm/2024/williams2024pgm-geometric/}
}