Distributional Sliced-Wasserstein and Applications to Generative Modeling

• URL: http://arxiv.org/abs/2002.07367v2
• Date: Sun, 4 Oct 2020 07:21:55 GMT
• Title: Distributional Sliced-Wasserstein and Applications to Generative Modeling
• Authors: Khai Nguyen and Nhat Ho and Tung Pham and Hung Bui
• Abstract summary: Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW) have been used widely in the recent years. We propose a novel distance, named Distributional Sliced-Wasserstein distance (DSW) 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.
• Score: 27.014748003733544
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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