New Asymptotic Analysis Simplifies Shapley Value for Large-Scale Dataset Valuation

A new paper from Tamine, Heymann, Vono, and Loiseau (arXiv:2607.03374) tackles the combinatorial complexity of the Shapley value for dataset valuation by deriving an asymptotic approximation. The traditional Shapley value requires evaluating all subsets of data sources, which becomes intractable as the number of datasets grows. The authors model utility as a smooth functional of empirical distributions via reproducing kernel Hilbert space (RKHS) mean embeddings and prove that the Shapley value converges to a simple leading term. This term captures the first-order contribution of each dataset relative to the surrounding data population, effectively identifying the asymptotically dominant factor.

The practical implication is significant for large-scale data markets and collaborative ML training where datasets are numerous. The leading term provides a tractable reference point that scales linearly with the number of data sources, allowing practitioners to quickly estimate relative dataset contributions without full combinatorial computation. Moreover, it offers a rigorous benchmark for evaluating existing Shapley value estimators, highlighting when approximations are accurate or biased. This work bridges theoretical game theory and applied data valuation, making fair compensation schemes more feasible for large data ecosystems.