Leveraging Optimal Transport for Distributed Two-Sample Testing: An Integrated Transportation Distance-based Framework

TL;DR

This paper proposes a new distributed two-sample testing framework using the Integrated Transportation Distance, enabling effective detection of distributional changes in decentralized data settings while maintaining privacy.

Contribution

It introduces the ITD framework based on optimal transport for distributed two-sample testing, with theoretical analysis and practical permutation testing procedures.

Findings

ITD achieves robust Type I error control

High power in detecting subtle distributional shifts

Effective in heterogeneous, high-dimensional data environments

Abstract

This paper introduces a novel framework for distributed two-sample testing using the Integrated Transportation Distance (ITD), an extension of the Optimal Transport distance. The approach addresses the challenges of detecting distributional changes in decentralized learning or federated learning environments, where data privacy and heterogeneity are significant concerns. We provide theoretical foundations for the ITD, including convergence properties and asymptotic behavior. A permutation test procedure is proposed for practical implementation in distributed settings, allowing for efficient computation while preserving data privacy. The framework's performance is demonstrated through theoretical power analysis and extensive simulations, showing robust Type I error control and high power across various distributions and dimensions. The results indicate that ITD effectively aggregates information across distributed clients, detecting subtle distributional shifts that might be missed when examining individual clients. This work contributes to the growing field of distributed statistical inference, offering a powerful tool for two-sample testing in modern, decentralized data environments.