- Recherche et sélection de publications
|
Generalized Sliced Wasserstein Distances
- Soheil Kolouri, Kimia Nadjahi #1, Umut Simsekli #1, Roland Badeau #1, Gustavo K. Rohde
-
| #1 |
Laboratoire traitement et communication de l'information (LTCI)
- Télécm ParisTech
- Institut Mines-Télécom
- Université Paris-Saclay
|
- References
- NeurIPS 2019, Vancouver, Canada, December 2019,
- Abstract
The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the Wasserstein distance, while being much simpler to compute, and is therefore used in various applications including generative modeling and general supervised/unsupervised learning. In this paper, we first clarify the mathematical connection between the SW distance and the Radon transform. We then utilize the generalized Radon transform to define a new family of distances for probability measures, which we call generalized sliced- Wasserstein (GSW) distances. We also show that, similar to the SW distance, the GSW distance can be extended to a maximum GSW (max-GSW) distance. We then provide the conditions under which GSW and max-GSW distances are indeed distances. Finally, we compare the numerical performance of the proposed distances on several generative modeling tasks, including SW flows and SW auto-encoders.
- Keywords
- Category
- Paper in proceedings
- Research Area(s)
- Engineering Sciences/Signal and Image processing
- Identifier(s)
-
Bibliographic key KN:NeurIPS-19b
- Export
-
- Last update
- on september 06, 2019 by Roland Badeau
|
