Multi-Dimensional Wasserstein Distance Implementation in Scipy

TL;DR

This paper introduces a new multi-dimensional Wasserstein distance function in Scipy, extending existing capabilities to handle complex distributions using linear programming, with thorough testing and planned integration into the main package.

Contribution

It presents the first multi-dimensional Wasserstein distance implementation in Scipy, transforming the problem into linear programming and integrating it into the main library.

Findings

Effective multi-dimensional Wasserstein distance computation using linear programming.

Implementation is accurate, reliable, and ready for inclusion in Scipy.

Enhances Scipy's statistical analysis tools for complex distributions.

Abstract

The Wasserstein distance, also known as the Earth mover distance or optimal transport distance, is a widely used measure of similarity between probability distributions. This paper presents an linear programming based implementation of the multi-dimensional Wasserstein distance function in Scipy, a powerful scientific computing package in Python. Building upon the existing one-dimensional scipy.stats.wasserstein_distance function, our work extends its capabilities to handle multi-dimensional distributions. To compute the multi-dimensional Wasserstein distance, we developed an implementation that transforms the problem into a linear programming problem. We utilized the scipy linear programming solver to effectively solve this transformed problem. The proposed implementation includes thorough documentation and comprehensive test cases to ensure accuracy and reliability. The resulting feature is set to be merged into the main Scipy development branch and will be included in the upcoming release, further enhancing the capabilities of Scipy in the field of multi-dimensional statistical analysis.