Keywords: Deep generative models, Sliced Wasserstein, Optimal Transport
Abstract: Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW), have been used widely in the recent years due to their fast computation and scalability even when the probability measures lie in a very high dimensional space. However, SW requires many unnecessary projection samples to approximate its value while Max-SW only uses the most important projection, which ignores the information of other useful directions. In order to account for these weaknesses, we propose a novel distance, named Distributional Sliced-Wasserstein distance (DSW), that finds an optimal distribution over projections that can balance between exploring distinctive projecting directions and the informativeness of projections themselves. We show that the DSW is a generalization of Max-SW, and it can be computed efficiently by searching for the optimal push-forward measure over a set of probability measures over the unit sphere satisfying certain regularizing constraints that favor distinct directions. Finally, we conduct extensive experiments with large-scale datasets to demonstrate the favorable performances of the proposed distances over the previous sliced-based distances in generative modeling applications.
One-sentence Summary: A new optimal transport distance based on slicing approach and its applications to generative modeling.
Supplementary Material: zip
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Data: [CIFAR-10](https://paperswithcode.com/dataset/cifar-10), [CelebA](https://paperswithcode.com/dataset/celeba), [LSUN](https://paperswithcode.com/dataset/lsun), [MNIST](https://paperswithcode.com/dataset/mnist)
Community Implementations: [![CatalyzeX](/images/catalyzex_icon.svg) 2 code implementations](https://www.catalyzex.com/paper/arxiv:2002.07367/code)