Distributional Sliced-Wasserstein and Applications to Generative Modeling
This work addresses a specific bottleneck in generative modeling for machine learning researchers, offering an incremental improvement over existing sliced-based distances.
The authors tackled the limitations of Sliced-Wasserstein and Max Sliced-Wasserstein distances in generative modeling by proposing Distributional Sliced-Wasserstein (DSW), which balances projection exploration and informativeness, and demonstrated its superior performance in experiments on large-scale datasets.
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.