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

TL;DR

This paper introduces an explainable AI approach to attribute Wasserstein distances to specific data components, enhancing understanding of dataset shifts and transport phenomena.

Contribution

It presents a novel method for interpreting Wasserstein distances, enabling attribution to data subgroups, features, or subspaces with high accuracy.

Findings

High accuracy across diverse datasets

Effective attribution to data components

Demonstrated utility in three use cases

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 plan (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 three use cases.