# Federated Measurement of Demographic Disparities from Quantile Sketches

arXiv: https://arxiv.org/abs/2602.18870 · HTML: https://mlsanity.com/paper/2602.18870/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 21 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [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)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Hidden Stratification Causes Clinically Meaningful Failures in Machine Learning for Medical Imaging](https://mlsanity.com/paper/1909.12475/) (2019)
- [Practical Secure Aggregation for Federated Learning on User-Held Data](https://mlsanity.com/paper/1611.04482/) (2016)
- [A survey on datasets for fairness-aware machine learning](https://mlsanity.com/paper/2110.00530/) (2021)
- [Ethical Machine Learning in Health Care](https://mlsanity.com/paper/2009.10576/) (2020)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Simple and near-optimal algorithms for hidden stratification and multi-group learning](https://mlsanity.com/paper/2112.12181/) (2021)
- [Optimal Quantile Approximation in Streams](https://mlsanity.com/paper/1603.05346/) (2016)
- [Computing Extremely Accurate Quantiles Using t-Digests](https://mlsanity.com/paper/1902.04023/) (2019)
- [Simpson's Paradox in Recommender Fairness: Reconciling differences between per-user and aggregated evaluations](https://mlsanity.com/paper/2210.07755/) (2022)

## Abstract (arXiv)

Many fairness goals are defined at a population level that misaligns with siloed data collection, which remains unsharable due to privacy regulations. Horizontal federated learning (FL) enables collaborative modeling across clients with aligned features without sharing raw data. We study federated auditing of demographic parity through score distributions, measuring disparity as a Wasserstein--Frechet variance between sensitive-group score laws, and expressing the population metric in federated form that makes explicit how silo-specific selection drives local-global mismatch. For the squared Wasserstein distance, we prove an ANOVA-style decomposition that separates (i) selection-induced mixture effects from (ii) cross-silo heterogeneity, yielding tight bounds linking local and global metrics. We then propose a one-shot, communication-efficient protocol in which each silo shares only group counts and a quantile summary of its local score distributions, enabling the server to estimate global disparity and its decomposition, with O(1/k) discretization bias (k quantiles) and finite-sample guarantees. Experiments on synthetic data and COMPAS show that a few dozen quantiles suffice to recover global disparity and diagnose its sources.