# Improving Fairness for Data Valuation in Horizontal Federated Learning

arXiv: https://arxiv.org/abs/2109.09046 · HTML: https://mlsanity.com/paper/2109.09046/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 19 Sep 2021.

## Builds on (most cited first, 28 of 28)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Federated Machine Learning: Concept and Applications](https://mlsanity.com/paper/1902.04885/) (2019)
- [Fair Resource Allocation in Federated Learning](https://mlsanity.com/paper/1905.10497/) (2019)
- [Client Selection for Federated Learning with Heterogeneous Resources in Mobile Edge](https://mlsanity.com/paper/1804.08333/) (2018)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Deep learning with noisy labels: exploring techniques and remedies in medical image analysis](https://mlsanity.com/paper/1912.02911/) (2019)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [Data Valuation using Reinforcement Learning](https://mlsanity.com/paper/1909.11671/) (2019)
- [Collaborative Fairness in Federated Learning](https://mlsanity.com/paper/2008.12161/) (2020)
- [Guaranteed Matrix Completion via Non-convex Factorization](https://mlsanity.com/paper/1411.8003/) (2014)
- [A Distributional Framework for Data Valuation](https://mlsanity.com/paper/2002.12334/) (2020)
- [Measure Contribution of Participants in Federated Learning](https://mlsanity.com/paper/1909.08525/) (2019)
- [Bounding the Estimation Error of Sampling-based Shapley Value Approximation](https://mlsanity.com/paper/1306.4265/) (2013)
- [A Survey on Data Pricing: from Economics to Data Science](https://mlsanity.com/paper/2009.04462/) (2020)
- [Efficient computation and analysis of distributional Shapley values](https://mlsanity.com/paper/2007.01357/) (2020)
- [Hierarchically Fair Federated Learning](https://mlsanity.com/paper/2004.10386/) (2020)
- [Training Fair Models in Federated Learning without Data Privacy Infringement](https://mlsanity.com/paper/2109.05662/) (2021)
- [Data Pricing in Machine Learning Pipelines](https://mlsanity.com/paper/2108.07915/) (2021)
- [Efficient Client Contribution Evaluation for Horizontal Federated Learning](https://mlsanity.com/paper/2102.13314/) (2021)

## Built on by (most cited first, 22 of 22)

- [Ten Challenging Problems in Federated Foundation Models](https://mlsanity.com/paper/2502.12176/) (2025)
- [Fair and efficient contribution valuation for vertical federated learning](https://mlsanity.com/paper/2201.02658/) (2022)
- [From Points to Coalitions: Hierarchical Contrastive Shapley Values for Prioritizing Data Samples](https://mlsanity.com/paper/2512.19363/) (2025)
- [Models of fairness in federated learning](https://mlsanity.com/paper/2112.00818/) (2021)
- [A Survey of Federated Evaluation in Federated Learning](https://mlsanity.com/paper/2305.08070/) (2023)
- [PeFAD: A Parameter-Efficient Federated Framework for Time Series Anomaly Detection](https://mlsanity.com/paper/2406.02318/) (2024)
- [FederatedTrust: A Solution for Trustworthy Federated Learning](https://mlsanity.com/paper/2302.09844/) (2023)
- [Aequa: Fair Model Rewards in Collaborative Learning via Slimmable Networks](https://mlsanity.com/paper/2502.04850/) (2025)
- [Mitigating Group Bias in Federated Learning for Heterogeneous Devices](https://mlsanity.com/paper/2309.07085/) (2023)
- [Secure and Verifiable Data Collaboration with Low-Cost Zero-Knowledge Proofs](https://mlsanity.com/paper/2311.15310/) (2023)
- [FedFair^3: Unlocking Threefold Fairness in Federated Learning](https://mlsanity.com/paper/2401.16350/) (2024)
- [ACE: A Model Poisoning Attack on Contribution Evaluation Methods in Federated Learning](https://mlsanity.com/paper/2405.20975/) (2024)
- [DeRDaVa: Deletion-Robust Data Valuation for Machine Learning](https://mlsanity.com/paper/2312.11413/) (2023)
- [Data valuation: The partial ordinal Shapley value for machine learning](https://mlsanity.com/paper/2305.01660/) (2023)
- [ROSS: RObust decentralized Stochastic learning based on Shapley values](https://mlsanity.com/paper/2411.00365/) (2024)
- [History-Aware and Dynamic Client Contribution in Federated Learning](https://mlsanity.com/paper/2403.07151/) (2024)
- [Online Prompt Pricing based on Combinatorial Multi-Armed Bandit and Hierarchical Stackelberg Game](https://mlsanity.com/paper/2405.15154/) (2024)
- [Dynamic Influence Tracker: Measuring Time-Varying Sample Influence During Training](https://mlsanity.com/paper/2502.10793/) (2025)
- [An Empirical Study of the Impact of Federated Learning on Machine Learning Model Accuracy](https://mlsanity.com/paper/2503.20768/) (2025)
- [Privacy-Preserving Feature Valuation in Vertical Federated Learning Using Shapley-CMI and PSI Permutation](https://mlsanity.com/paper/2512.14767/) (2025)
- [When the Server Steps In: Calibrated Updates for Fair Federated Learning](https://mlsanity.com/paper/2601.05352/) (2026)
- [Compressed Proximal Federated Learning for Non-Convex Composite Optimization on Heterogeneous Data](https://mlsanity.com/paper/2603.07654/) (2026)

## Abstract (arXiv)

Federated learning is an emerging decentralized machine learning scheme that allows multiple data owners to work collaboratively while ensuring data privacy. The success of federated learning depends largely on the participation of data owners. To sustain and encourage data owners' participation, it is crucial to fairly evaluate the quality of the data provided by the data owners and reward them correspondingly. Federated Shapley value, recently proposed by Wang et al. [Federated Learning, 2020], is a measure for data value under the framework of federated learning that satisfies many desired properties for data valuation. However, there are still factors of potential unfairness in the design of federated Shapley value because two data owners with the same local data may not receive the same evaluation. We propose a new measure called completed federated Shapley value to improve the fairness of federated Shapley value. The design depends on completing a matrix consisting of all the possible contributions by different subsets of the data owners. It is shown under mild conditions that this matrix is approximately low-rank by leveraging concepts and tools from optimization. Both theoretical analysis and empirical evaluation verify that the proposed measure does improve fairness in many circumstances.