Sliced Wasserstein Kernels for Probability Distributions

TL;DR

This paper introduces a new family of positive definite kernels based on the Sliced Wasserstein distance, enhancing kernel methods for probability distributions in machine learning.

Contribution

It provides the first provably positive definite kernels derived from the Sliced Wasserstein distance for use in kernel methods.

Findings

Improved performance in learning tasks using Sliced Wasserstein kernels

Theoretical guarantees of positive definiteness

Enhanced computational efficiency for optimal transport distances

Abstract

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on alternative formulations of the optimal transport have allowed for faster solutions to the problem and has revamped its 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.