# The Fair Value of Data Under Heterogeneous Privacy Constraints in Federated Learning

arXiv: https://arxiv.org/abs/2301.13336 · HTML: https://mlsanity.com/paper/2301.13336/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 19 of 19)

- [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)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [A Distributional Framework for Data Valuation](https://mlsanity.com/paper/2002.12334/) (2020)
- [Model-sharing Games: Analyzing Federated Learning Under Voluntary Participation](https://mlsanity.com/paper/2010.00753/) (2020)
- [Privacy Loss in Apple's Implementation of Differential Privacy on MacOS 10.12](https://mlsanity.com/paper/1709.02753/) (2017)
- [Mechanisms that Incentivize Data Sharing in Federated Learning](https://mlsanity.com/paper/2207.04557/) (2022)
- [Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms](https://mlsanity.com/paper/2201.03968/) (2022)
- [Learning to Generate Image Embeddings with User-level Differential Privacy](https://mlsanity.com/paper/2211.10844/) (2022)
- [Trading Data For Learning: Incentive Mechanism For On-Device Federated Learning](https://mlsanity.com/paper/2009.05604/) (2020)
- [Optimal Data Acquisition with Privacy-Aware Agents](https://mlsanity.com/paper/2209.06340/) (2022)
- [Optimal Data Acquisition for Statistical Estimation](https://mlsanity.com/paper/1711.01295/) (2017)
- [Prior-free Data Acquisition for Accurate Statistical Estimation](https://mlsanity.com/paper/1811.12655/) (2018)
- [Achieving Data Utility-Privacy Tradeoff in Internet of Medical Things: A Machine Learning Approach](https://mlsanity.com/paper/1902.02898/) (2019)

## Built on by (most cited first, 5 of 5)

- [Threshold KNN-Shapley: A Linear-Time and Privacy-Friendly Approach to Data Valuation](https://mlsanity.com/paper/2308.15709/) (2023)
- [Learning to Understand: Identifying Interactions via the M"obius Transform](https://mlsanity.com/paper/2402.02631/) (2024)
- [Noise-Aware Algorithm for Heterogeneous Differentially Private Federated Learning](https://mlsanity.com/paper/2406.03519/) (2024)
- [Private Estimation when Data and Privacy Demands are Correlated](https://mlsanity.com/paper/2407.11274/) (2024)
- [A case for data valuation transparency via DValCards](https://mlsanity.com/paper/2506.23349/) (2025)

## Abstract (arXiv)

Modern data aggregation often involves a platform collecting data from a network of users with various privacy options. Platforms must solve the problem of how to allocate incentives to users to convince them to share their data. This paper puts forth an idea for a textitfair amount to compensate users for their data at a given privacy level based on an axiomatic definition of fairness, along the lines of the celebrated Shapley value. To the best of our knowledge, these are the first fairness concepts for data that explicitly consider privacy constraints. We also formulate a heterogeneous federated learning problem for the platform with privacy level options for users. By studying this problem, we investigate the amount of compensation users receive under fair allocations with different privacy levels, amounts of data, and degrees of heterogeneity. We also discuss what happens when the platform is forced to design fair incentives. Under certain conditions we find that when privacy sensitivity is low, the platform will set incentives to ensure that it collects all the data with the lowest privacy options. When the privacy sensitivity is above a given threshold, the platform will provide no incentives to users. Between these two extremes, the platform will set the incentives so some fraction of the users chooses the higher privacy option and the others chooses the lower privacy option.