# 2D-Shapley: A Framework for Fragmented Data Valuation

arXiv: https://arxiv.org/abs/2306.10473 · HTML: https://mlsanity.com/paper/2306.10473/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 18 Jun 2023.

## Builds on (most cited first, 14 of 14)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [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)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [Data Valuation using Reinforcement Learning](https://mlsanity.com/paper/1909.11671/) (2019)
- [LAVA: Data Valuation without Pre-Specified Learning Algorithms](https://mlsanity.com/paper/2305.00054/) (2023)
- [Measuring the Effect of Training Data on Deep Learning Predictions via Randomized Experiments](https://mlsanity.com/paper/2206.10013/) (2022)
- [Data Valuation for Medical Imaging Using Shapley Value: Application on A Large-scale Chest X-ray Dataset](https://mlsanity.com/paper/2010.08006/) (2020)
- [Incentivizing Collaboration in Machine Learning via Synthetic Data Rewards](https://mlsanity.com/paper/2112.09327/) (2021)
- [Data Debugging with Shapley Importance over End-to-End Machine Learning Pipelines](https://mlsanity.com/paper/2204.11131/) (2022)
- [Who's responsible? Jointly quantifying the contribution of the learning algorithm and training data](https://mlsanity.com/paper/1910.04214/) (2019)

## Built on by (most cited first, 7 of 7)

- [Efficient Data Shapley for Weighted Nearest Neighbor Algorithms](https://mlsanity.com/paper/2401.11103/) (2024)
- [2D-OOB: Attributing Data Contribution Through Joint Valuation Framework](https://mlsanity.com/paper/2408.03572/) (2024)
- [Towards Data Valuation via Asymmetric Data Shapley](https://mlsanity.com/paper/2411.00388/) (2024)
- [Learning Counterfactual Outcomes Under Rank Preservation](https://mlsanity.com/paper/2502.06398/) (2025)
- [Chunked Data Shapley: A Scalable Dataset Quality Assessment for Machine Learning](https://mlsanity.com/paper/2508.16255/) (2025)
- [Hierarchical Dataset Selection for High-Quality Data Sharing](https://mlsanity.com/paper/2512.10952/) (2025)
- [On the Fragility of Data Attribution When Learning Is Distributed](https://mlsanity.com/paper/2605.15520/) (2026)

## Abstract (arXiv)

Data valuation -- quantifying the contribution of individual data sources to certain predictive behaviors of a model -- is of great importance to enhancing the transparency of machine learning and designing incentive systems for data sharing. Existing work has focused on evaluating data sources with the shared feature or sample space. How to valuate fragmented data sources of which each only contains partial features and samples remains an open question. We start by presenting a method to calculate the counterfactual of removing a fragment from the aggregated data matrix. Based on the counterfactual calculation, we further propose 2D-Shapley, a theoretical framework for fragmented data valuation that uniquely satisfies some appealing axioms in the fragmented data context. 2D-Shapley empowers a range of new use cases, such as selecting useful data fragments, providing interpretation for sample-wise data values, and fine-grained data issue diagnosis.