An Asymptotic Analysis of the Shapley Value for Dataset Valuation

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.