# Data valuation: The partial ordinal Shapley value for machine learning

arXiv: https://arxiv.org/abs/2305.01660 · HTML: https://mlsanity.com/paper/2305.01660/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 17 of 17)

- [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)
- [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)
- [Data Valuation using Reinforcement Learning](https://mlsanity.com/paper/1909.11671/) (2019)
- [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)
- [Shapley Q-value: A Local Reward Approach to Solve Global Reward Games](https://mlsanity.com/paper/1907.05707/) (2019)
- [Bounding the Estimation Error of Sampling-based Shapley Value Approximation](https://mlsanity.com/paper/1306.4265/) (2013)
- [Model-based Pricing for Machine Learning in a Data Marketplace](https://mlsanity.com/paper/1805.11450/) (2018)
- [Data Valuation for Medical Imaging Using Shapley Value: Application on A Large-scale Chest X-ray Dataset](https://mlsanity.com/paper/2010.08006/) (2020)
- [Improving Fairness for Data Valuation in Horizontal Federated Learning](https://mlsanity.com/paper/2109.09046/) (2021)
- [Data Pricing in Machine Learning Pipelines](https://mlsanity.com/paper/2108.07915/) (2021)
- [Fair and efficient contribution valuation for vertical federated learning](https://mlsanity.com/paper/2201.02658/) (2022)
- [Is Shapley Value fair? Improving Client Selection for Mavericks in Federated Learning](https://mlsanity.com/paper/2106.10734/) (2021)

## Built on by (most cited first, 1 of 1)

- [Incentivizing Time-Aware Fairness in Data Sharing](https://mlsanity.com/paper/2510.09240/) (2025)

## Abstract (arXiv)

Data valuation using Shapley value has emerged as a prevalent research domain in machine learning applications. However, it is a challenge to address the role of order in data cooperation as most research lacks such discussion. To tackle this problem, this paper studies the definition of the partial ordinal Shapley value by group theory in abstract algebra. Besides, since the calculation of the partial ordinal Shapley value requires exponential time, this paper also gives three algorithms for approximating the results. The Truncated Monte Carlo algorithm is derived from the classic Shapley value approximation algorithm. The Classification Monte Carlo algorithm and the Classification Truncated Monte Carlo algorithm are based on the fact that the data points in the same class provide similar information, then we can accelerate the calculation by leaving out some data points in each class.