Generalized Sliced Wasserstein Distances

By Soheil Kolouri, Kimia Nadjahi, Umut Simsekli, Roland Badeau, Gustavo Kunde Rohde. Neural Information Processing Systems, 2019

389 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/d19d26d45e0ff2b1d0c46264cc12e75762f16daf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yifan Zhang
2. Jian Liang
3. Jiashi Feng
4. Dapeng Hu
5. Fei Chen
6. Alexander Tong
7. Romy Mi Luo
8. Jessie Huang

In Computational Mechanics

1. Jian Liang
2. Jiashi Feng

In Computer Vision and Pattern Recognition

1. Yifan Zhang
2. Jian Liang
3. Dapeng Hu
4. Jiashi Feng
5. Romy Mi Luo
6. Fei Chen
7. Alexander Tong
8. Jessie Huang

Citations in the corpus

• TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics (2020, background): “Recent effort approximates OT on subspaces (Muzellec & Cuturi, 2019) or even a single dimension (Kolouri et al., 2019).”
• No Fear of Heterogeneity: Classifier Calibration for Federated Learning with Non-IID Data (2021, methodology): “We resort to Sliced Wasserstein Distance [45], which is a popular metric to measure the distances between distributions, to quantify the separability of GMM.”