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

arXiv: https://arxiv.org/abs/2506.16047 · HTML: https://mlsanity.com/paper/2506.16047/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [Towards Understanding Camera Motions in Any Video](https://mlsanity.com/paper/2504.15376/) (2025)
- [MENTOR: Multi-level Self-supervised Learning for Multimodal Recommendation](https://mlsanity.com/paper/2402.19407/) (2024)
- [An improved central limit theorem and fast convergence rates for entropic transportation costs](https://mlsanity.com/paper/2204.09105/) (2022)
- [AlignGroup: Learning and Aligning Group Consensus with Member Preferences for Group Recommendation](https://mlsanity.com/paper/2409.02580/) (2024)
- [An Integrated Transportation Distance Between Kernels and Approximate Dynamic Risk Evaluation in Markov Systems](https://mlsanity.com/paper/2311.06645/) (2023)
- [Federated Nonparametric Hypothesis Testing with Differential Privacy Constraints: Optimal Rates and Adaptive Tests](https://mlsanity.com/paper/2406.06749/) (2024)
- [Multi-Cali Anything: Dense Feature Multi-Frame Structure-from-Motion for Large-Scale Camera Array Calibration](https://mlsanity.com/paper/2503.00737/) (2025)
- [Integrative High Dimensional Multiple Testing with Heterogeneity under Data Sharing Constraints](https://mlsanity.com/paper/2004.00816/) (2020)
- [Fast Dual Subgradient Optimization of the Integrated Transportation Distance Between Stochastic Kernels](https://mlsanity.com/paper/2312.01432/) (2023)
- [MDVT: Enhancing Multimodal Recommendation with Model-Agnostic Multimodal-Driven Virtual Triplets](https://mlsanity.com/paper/2505.16665/) (2025)
- [Statistical inferences for complex dependence of multimodal imaging data](https://mlsanity.com/paper/2303.03582/) (2023)

## Built on by (most cited first, 1 of 1)

- [Spec-LLaVA: Accelerating Vision-Language Models with Dynamic Tree-Based Speculative Decoding](https://mlsanity.com/paper/2509.11961/) (2025)

## Abstract (arXiv)

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.