Wasserstein Distances Made Explainable: Insights into Dataset Shifts and Transport Phenomena

Abstract

Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing the corresponding transport map (or coupling) may not be sufficient for understanding what factors contribute to a high or low Wasserstein distance. In this work, we propose a novel solution based on Explainable AI that allows us to efficiently and accurately attribute Wasserstein distances to various data components, including data subgroups, input features, or interpretable subspaces. Our method achieves high accuracy across diverse datasets and Wasserstein distance specifications, and its practical utility is demonstrated in two use cases.