# A Distributional Framework for Data Valuation

arXiv: https://arxiv.org/abs/2002.12334 · HTML: https://mlsanity.com/paper/2002.12334/

## Key facts

- Cited by 80 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2020.

## Built on by (most cited first, 30 of 80)

- [Data-centric Artificial Intelligence: A Survey](https://mlsanity.com/paper/2303.10158/) (2023)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [Fair Federated Medical Image Segmentation via Client Contribution Estimation](https://mlsanity.com/paper/2303.16520/) (2023)
- [Measuring the Effect of Training Data on Deep Learning Predictions via Randomized Experiments](https://mlsanity.com/paper/2206.10013/) (2022)
- [Data-OOB: Out-of-bag Estimate as a Simple and Efficient Data Value](https://mlsanity.com/paper/2304.07718/) (2023)
- [WeightedSHAP: analyzing and improving Shapley based feature attributions](https://mlsanity.com/paper/2209.13429/) (2022)
- [CS-Shapley: Class-wise Shapley Values for Data Valuation in Classification](https://mlsanity.com/paper/2211.06800/) (2022)
- [Explaining Latent Representations with a Corpus of Examples](https://mlsanity.com/paper/2110.15355/) (2021)
- [Interpretable Data-Based Explanations for Fairness Debugging](https://mlsanity.com/paper/2112.09745/) (2021)
- [Rethinking Data Shapley for Data Selection Tasks: Misleads and Merits](https://mlsanity.com/paper/2405.03875/) (2024)
- [Data Shapley Valuation for Efficient Batch Active Learning](https://mlsanity.com/paper/2104.08312/) (2021)
- [Improving Fairness for Data Valuation in Horizontal Federated Learning](https://mlsanity.com/paper/2109.09046/) (2021)
- [Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attribution](https://mlsanity.com/paper/2401.15866/) (2024)
- [Incentivizing Collaboration in Machine Learning via Synthetic Data Rewards](https://mlsanity.com/paper/2112.09327/) (2021)
- [On the Trade-Off between Actionable Explanations and the Right to be Forgotten](https://mlsanity.com/paper/2208.14137/) (2022)
- [Threshold KNN-Shapley: A Linear-Time and Privacy-Friendly Approach to Data Valuation](https://mlsanity.com/paper/2308.15709/) (2023)
- [Better, Not Just More: Data-Centric Machine Learning for Earth Observation](https://mlsanity.com/paper/2312.05327/) (2023)
- [Fair and efficient contribution valuation for vertical federated learning](https://mlsanity.com/paper/2201.02658/) (2022)
- [Efficient Data Shapley for Weighted Nearest Neighbor Algorithms](https://mlsanity.com/paper/2401.11103/) (2024)
- [Variance reduced Shapley value estimation for trustworthy data valuation](https://mlsanity.com/paper/2210.16835/) (2022)
- [Label-Free Explainability for Unsupervised Models](https://mlsanity.com/paper/2203.01928/) (2022)
- [Efficient XAI Techniques: A Taxonomic Survey](https://mlsanity.com/paper/2302.03225/) (2023)
- [Learning to Understand: Identifying Interactions via the M"obius Transform](https://mlsanity.com/paper/2402.02631/) (2024)
- [DU-Shapley: A Shapley Value Proxy for Efficient Dataset Valuation](https://mlsanity.com/paper/2306.02071/) (2023)
- [A Note on "Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms"](https://mlsanity.com/paper/2304.04258/) (2023)
- [SHAPr: An Efficient and Versatile Membership Privacy Risk Metric for Machine Learning](https://mlsanity.com/paper/2112.02230/) (2021)
- [Sample based Explanations via Generalized Representers](https://mlsanity.com/paper/2310.18526/) (2023)

## Abstract (arXiv)

Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its foundational role, a key limitation of the data Shapley framework is that it only provides valuations for points within a fixed data set. It does not account for statistical aspects of the data and does not give a way to reason about points outside the data set. To address these limitations, we propose a novel framework -- distributional Shapley -- where the value of a point is defined in the context of an underlying data distribution. We prove that distributional Shapley has several desirable statistical properties; for example, the values are stable under perturbations to the data points themselves and to the underlying data distribution. We leverage these properties to develop a new algorithm for estimating values from data, which comes with formal guarantees and runs two orders of magnitude faster than state-of-the-art algorithms for computing the (non-distributional) data Shapley values. We apply distributional Shapley to diverse data sets and demonstrate its utility in a data market setting.