# Towards Efficient Data Valuation Based on the Shapley Value

arXiv: https://arxiv.org/abs/1902.10275 · HTML: https://mlsanity.com/paper/1902.10275/

## Key facts

- Cited by 281 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 30 of 281)

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- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions](https://mlsanity.com/paper/2405.13954/) (2024)
- [DataPerf: Benchmarks for Data-Centric AI Development](https://mlsanity.com/paper/2207.10062/) (2022)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
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- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [LAVA: Data Valuation without Pre-Specified Learning Algorithms](https://mlsanity.com/paper/2305.00054/) (2023)
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- [Fair Federated Medical Image Segmentation via Client Contribution Estimation](https://mlsanity.com/paper/2303.16520/) (2023)
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- [One for One, or All for All: Equilibria and Optimality of Collaboration in Federated Learning](https://mlsanity.com/paper/2103.03228/) (2021)
- [Mechanisms that Incentivize Data Sharing in Federated Learning](https://mlsanity.com/paper/2207.04557/) (2022)
- [HYDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks](https://mlsanity.com/paper/2102.02515/) (2021)
- [A Comprehensive Survey of Incentive Mechanism for Federated Learning](https://mlsanity.com/paper/2106.15406/) (2021)
- [Data-OOB: Out-of-bag Estimate as a Simple and Efficient Data Value](https://mlsanity.com/paper/2304.07718/) (2023)
- [First is Better Than Last for Language Data Influence](https://mlsanity.com/paper/2202.11844/) (2022)
- [Training Data Attribution via Approximate Unrolled Differentiation](https://mlsanity.com/paper/2405.12186/) (2024)
- [CS-Shapley: Class-wise Shapley Values for Data Valuation in Classification](https://mlsanity.com/paper/2211.06800/) (2022)

## Abstract (arXiv)

"How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining prospective compensation when data breaches happen. In this paper, we study the problem of data valuation by utilizing the Shapley value, a popular notion of value which originated in cooperative game theory. The Shapley value defines a unique payoff scheme that satisfies many desiderata for the notion of data value. However, the Shapley value often requires exponential time to compute. To meet this challenge, we propose a repertoire of efficient algorithms for approximating the Shapley value. We also demonstrate the value of each training instance for various benchmark datasets.