# Probably Approximate Shapley Fairness with Applications in Machine Learning

arXiv: https://arxiv.org/abs/2212.00630 · HTML: https://mlsanity.com/paper/2212.00630/

## Key facts

- Cited by 6 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 1 Dec 2022.

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

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Convolutional Neural Networks for Sentence Classification](https://mlsanity.com/paper/1408.5882/) (2014)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [A Distributional Framework for Data Valuation](https://mlsanity.com/paper/2002.12334/) (2020)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)
- [Collaborative Machine Learning with Incentive-Aware Model Rewards](https://mlsanity.com/paper/2010.12797/) (2020)
- [Bounding the Estimation Error of Sampling-based Shapley Value Approximation](https://mlsanity.com/paper/1306.4265/) (2013)
- [A Multilinear Sampling Algorithm to Estimate Shapley Values](https://mlsanity.com/paper/2010.12082/) (2020)
- [Data Shapley Valuation for Efficient Batch Active Learning](https://mlsanity.com/paper/2104.08312/) (2021)
- [Incentivizing Collaboration in Machine Learning via Synthetic Data Rewards](https://mlsanity.com/paper/2112.09327/) (2021)
- [Collaborative Machine Learning Markets with Data-Replication-Robust Payments](https://mlsanity.com/paper/1911.09052/) (2019)
- [Energy-Based Learning for Cooperative Games, with Applications to Valuation Problems in Machine Learning](https://mlsanity.com/paper/2106.02938/) (2021)
- [On the Convergence of the Shapley Value in Parametric Bayesian Learning Games](https://mlsanity.com/paper/2205.07428/) (2022)

## Built on by (most cited first, 6 of 6)

- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [Fair yet Asymptotically Equal Collaborative Learning](https://mlsanity.com/paper/2306.05764/) (2023)
- [DETAIL: Task DEmonsTration Attribution for Interpretable In-context Learning](https://mlsanity.com/paper/2405.14899/) (2024)
- [Data value estimation on private gradients](https://mlsanity.com/paper/2412.17008/) (2024)
- [CoAst: Validation-Free Contribution Assessment for Federated Learning based on Cross-Round Valuation](https://mlsanity.com/paper/2409.02495/) (2024)
- [A case for data valuation transparency via DValCards](https://mlsanity.com/paper/2506.23349/) (2025)

## Abstract (arXiv)

The Shapley value (SV) is adopted in various scenarios in machine learning (ML), including data valuation, agent valuation, and feature attribution, as it satisfies their fairness requirements. However, as exact SVs are infeasible to compute in practice, SV estimates are approximated instead. This approximation step raises an important question: do the SV estimates preserve the fairness guarantees of exact SVs? We observe that the fairness guarantees of exact SVs are too restrictive for SV estimates. Thus, we generalise Shapley fairness to probably approximate Shapley fairness and propose fidelity score, a metric to measure the variation of SV estimates, that determines how probable the fairness guarantees hold. Our last theoretical contribution is a novel greedy active estimation (GAE) algorithm that will maximise the lowest fidelity score and achieve a better fairness guarantee than the de facto Monte-Carlo estimation. We empirically verify GAE outperforms several existing methods in guaranteeing fairness while remaining competitive in estimation accuracy in various ML scenarios using real-world datasets.