An Asymptotic Analysis of the Shapley Value for Dataset Valuation

2026-07-03

AI Summary

This work addresses the high computational complexity of Shapley value estimation in large-scale data valuation by modeling the utility function as a smooth functional of the mean embedding of empirical distributions in a reproducing kernel Hilbert space (RKHS). Leveraging tools from functional analysis and cooperative game theory, the authors conduct an asymptotic analysis that reveals how, as the number of data sources grows, the Shapley value is asymptotically characterized by a simple first-order dominant term. This finding elucidates the scaling behavior and structural properties of Shapley values in such settings. Building on this insight, the paper derives an interpretable and computationally tractable approximation, which not only provides a theoretical benchmark for existing estimation algorithms but also offers a principled foundation for efficient and reliable valuation in large-scale data markets.

Abstract

We propose an asymptotic analysis of the Shapley value in a dataset valuation setting in which utilities are modeled as smooth functionals of empirical distributions via reproducing kernel Hilbert space (RKHS) mean embeddings. We prove that, despite its combinatorial definition, the Shapley value of a data source is asymptotically captured by a simple leading term. This term can be interpreted as the first-order contribution of a dataset relative to the surrounding data population. It also identifies the scale of the Shapley value as the number of data sources grows and provides a framework for analyzing existing Shapley value estimators. Moreover, for practitioners working with large numbers of datasets, the leading term becomes a tractable reference against which Shapley value approximations can be benchmarked.

Problem

• Shapley value
• dataset valuation
• asymptotic analysis
• RKHS mean embeddings
• data valuation

Innovation

• Shapley value
• asymptotic analysis
• dataset valuation
• RKHS mean embedding
• leading term