Sliced Wasserstein Kernels for Probability Distributions

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as powerful discrepancy measures for probability distributions. The recent developments on alternative formulations of the optimal transport have allowed for faster solutions to the problem and have revamped their practical applications in machine learning. In this paper, we exploit the widely used kernel methods and provide a family of provably positive definite kernels based on the Sliced Wasserstein distance and demonstrate the benefits of these kernels in a variety of learning tasks. Our work provides a new perspective on the application of optimal transport flavored distances through kernel methods in machine learning tasks.