# Fair and efficient contribution valuation for vertical federated learning

arXiv: https://arxiv.org/abs/2201.02658 · HTML: https://mlsanity.com/paper/2201.02658/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 58 references that are in the map.
- First posted on arXiv 7 Jan 2022.

## Builds on (most cited first, 21 of 21)

- [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)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [SecureBoost: A Lossless Federated Learning Framework](https://mlsanity.com/paper/1901.08755/) (2019)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [Federated Learning over Wireless Networks: Convergence Analysis and Resource Allocation](https://mlsanity.com/paper/1910.13067/) (2019)
- [VAFL: a Method of Vertical Asynchronous Federated Learning](https://mlsanity.com/paper/2007.06081/) (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)
- [GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2109.02053/) (2021)
- [SGD without Replacement: Sharper Rates for General Smooth Convex Functions](https://mlsanity.com/paper/1903.01463/) (2019)
- [Generalized Low Rank Models](https://mlsanity.com/paper/1410.0342/) (2014)
- [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)
- [Improving Fairness for Data Valuation in Horizontal Federated Learning](https://mlsanity.com/paper/2109.09046/) (2021)
- [Privacy-Preserving Asynchronous Federated Learning Algorithms for Multi-Party Vertically Collaborative Learning](https://mlsanity.com/paper/2008.06233/) (2020)
- [Feature-Distributed SVRG for High-Dimensional Linear Classification](https://mlsanity.com/paper/1802.03604/) (2018)

## Built on by (most cited first, 18 of 18)

- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [Advances and Open Challenges in Federated Foundation Models](https://mlsanity.com/paper/2404.15381/) (2024)
- [Vertical Federated Learning: A Structured Literature Review](https://mlsanity.com/paper/2212.00622/) (2022)
- [Vertical Federated Learning for Effectiveness, Security, Applicability: A Survey](https://mlsanity.com/paper/2405.17495/) (2024)
- [Towards Interpretable Federated Learning](https://mlsanity.com/paper/2302.13473/) (2023)
- [Online Vertical Federated Learning for Cooperative Spectrum Sensing](https://mlsanity.com/paper/2312.11363/) (2023)
- [A Survey on Contribution Evaluation in Vertical Federated Learning](https://mlsanity.com/paper/2405.02364/) (2024)
- [ACE: A Model Poisoning Attack on Contribution Evaluation Methods in Federated Learning](https://mlsanity.com/paper/2405.20975/) (2024)
- [Entropy-driven Fair and Effective Federated Learning](https://mlsanity.com/paper/2301.12407/) (2023)
- [Vertical Federated Learning in Practice: The Good, the Bad, and the Ugly](https://mlsanity.com/paper/2502.08160/) (2025)
- [Incentive Allocation in Vertical Federated Learning Based on Bankruptcy Problem](https://mlsanity.com/paper/2307.03515/) (2023)
- [Data valuation: The partial ordinal Shapley value for machine learning](https://mlsanity.com/paper/2305.01660/) (2023)
- [VFL-RPS: Relevant Participant Selection in Vertical Federated Learning](https://mlsanity.com/paper/2502.14375/) (2025)
- [Game of Privacy: Towards Better Federated Platform Collaboration under Privacy Restriction](https://mlsanity.com/paper/2202.05139/) (2022)
- [Owen Sampling Accelerates Contribution Estimation in Federated Learning](https://mlsanity.com/paper/2508.21261/) (2025)
- [Privacy-Preserving Feature Valuation in Vertical Federated Learning Using Shapley-CMI and PSI Permutation](https://mlsanity.com/paper/2512.14767/) (2025)
- [On the Fragility of Data Attribution When Learning Is Distributed](https://mlsanity.com/paper/2605.15520/) (2026)
- [SwarmHarness: Skill-Based Task Routing via Decentralized Incentive-Aligned AI Agent Networks](https://mlsanity.com/paper/2605.28764/) (2026)

## Abstract (arXiv)

Federated learning is an emerging technology for training machine learning models across decentralized data sources without sharing data. Vertical federated learning, also known as feature-based federated learning, applies to scenarios where data sources have the same sample IDs but different feature sets. To ensure fairness among data owners, it is critical to objectively assess the contributions from different data sources and compensate the corresponding data owners accordingly. The Shapley value is a provably fair contribution valuation metric originating from cooperative game theory. However, its straight-forward computation requires extensively retraining a model on each potential combination of data sources, leading to prohibitively high communication and computation overheads due to multiple rounds of federated learning. To tackle this challenge, we propose a contribution valuation metric called vertical federated Shapley value (VerFedSV) based on the classic Shapley value. We show that VerFedSV not only satisfies many desirable properties of fairness but is also efficient to compute. Moreover, VerFedSV can be adapted to both synchronous and asynchronous vertical federated learning algorithms. Both theoretical analysis and extensive experimental results demonstrate the fairness, efficiency, adaptability, and effectiveness of VerFedSV.