# Federated Wasserstein Distance

arXiv: https://arxiv.org/abs/2310.01973 · HTML: https://mlsanity.com/paper/2310.01973/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [On Coresets for Logistic Regression](https://mlsanity.com/paper/1805.08571/) (2018)
- [Manifold Interpolating Optimal-Transport Flows for Trajectory Inference](https://mlsanity.com/paper/2206.14928/) (2022)
- [Coresets and Sketches](https://mlsanity.com/paper/1601.00617/) (2016)
- [Learning Wasserstein Embeddings](https://mlsanity.com/paper/1710.07457/) (2017)
- [Wasserstein Measure Coresets](https://mlsanity.com/paper/1805.07412/) (2018)
- [Diffeomorphic density matching by optimal information transport](https://mlsanity.com/paper/1501.07635/) (2015)

## Built on by (most cited first, 8 of 8)

- [Data Valuation and Detections in Federated Learning](https://mlsanity.com/paper/2311.05304/) (2023)
- [A Universal Metric of Dataset Similarity for Cross-silo Federated Learning](https://mlsanity.com/paper/2404.18773/) (2024)
- [When Sample Selection Bias Precipitates Model Collapse](https://mlsanity.com/paper/2606.13732/) (2026)
- [Sublinear Algorithms for Wasserstein and Total Variation Distances: Applications to Fairness and Privacy Auditing](https://mlsanity.com/paper/2503.07775/) (2025)
- [Personalized Federated Learning under Model Dissimilarity Constraints](https://mlsanity.com/paper/2505.07575/) (2025)
- [ATR-Bench: A Federated Learning Benchmark for Adaptation, Trust, and Reasoning](https://mlsanity.com/paper/2505.16850/) (2025)
- [Data Valuation and Selection in a Federated Model Marketplace](https://mlsanity.com/paper/2509.18104/) (2025)
- [Highly Data Parallelizable Estimation of the Sliced-Wasserstein Distance Using Cumulative Distribution Functions](https://mlsanity.com/paper/2606.30310/) (2026)

## Abstract (arXiv)

We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients whilst a central entity/server orchestrates the computations (again, without having access to the samples). To achieve this feat, we take advantage of the geometric properties of the Wasserstein distance -- in particular, the triangle inequality -- and that of the associated em geodesics: our algorithm, FedWad (for Federated Wasserstein Distance), iteratively approximates the Wasserstein distance by manipulating and exchanging distributions from the space of geodesics in lieu of the input samples. In addition to establishing the convergence properties of FedWad, we provide empirical results on federated coresets and federate optimal transport dataset distance, that we respectively exploit for building a novel federated model and for boosting performance of popular federated learning algorithms.