Riemannian Convex Potential Maps

Samuel Cohen, Brandon Amos, Yaron Lipman
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:2028-2038, 2021.

Abstract

Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational tradeoffs. We propose and study a class of flows that uses convex potentials from Riemannian optimal transport. These are universal and can model distributions on any compact Riemannian manifold without requiring domain knowledge of the manifold to be integrated into the architecture. We demonstrate that these flows can model standard distributions on spheres, and tori, on synthetic and geological data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-cohen21a, title = {Riemannian Convex Potential Maps}, author = {Cohen, Samuel and Amos, Brandon and Lipman, Yaron}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {2028--2038}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/cohen21a/cohen21a.pdf}, url = {https://proceedings.mlr.press/v139/cohen21a.html}, abstract = {Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational tradeoffs. We propose and study a class of flows that uses convex potentials from Riemannian optimal transport. These are universal and can model distributions on any compact Riemannian manifold without requiring domain knowledge of the manifold to be integrated into the architecture. We demonstrate that these flows can model standard distributions on spheres, and tori, on synthetic and geological data.} }
Endnote
%0 Conference Paper %T Riemannian Convex Potential Maps %A Samuel Cohen %A Brandon Amos %A Yaron Lipman %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-cohen21a %I PMLR %P 2028--2038 %U https://proceedings.mlr.press/v139/cohen21a.html %V 139 %X Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational tradeoffs. We propose and study a class of flows that uses convex potentials from Riemannian optimal transport. These are universal and can model distributions on any compact Riemannian manifold without requiring domain knowledge of the manifold to be integrated into the architecture. We demonstrate that these flows can model standard distributions on spheres, and tori, on synthetic and geological data.
APA
Cohen, S., Amos, B. & Lipman, Y.. (2021). Riemannian Convex Potential Maps. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:2028-2038 Available from https://proceedings.mlr.press/v139/cohen21a.html.

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