From Points to Coalitions: Hierarchical Contrastive Shapley Values for Prioritizing Data Samples

Abstract

How should we quantify the value of each training example when datasets are large, heterogeneous, and geometrically structured? Classical Data-Shapley answers in principle, but its O(n!) complexity and point-wise perspective are ill-suited to modern scales. We propose Hierarchical Contrastive Data Valuation (HCDV), a three-stage framework that (i) learns a contrastive, geometry-preserving representation, (ii) organizes the data into a balanced coarse-to-fine hierarchy of clusters, and (iii) assigns Shapley-style payoffs to coalitions via local Monte-Carlo games whose budgets are propagated downward. HCDV collapses the factorial burden to O(T sum_{l} K_{l}) = O(T K_max log n), rewards examples that sharpen decision boundaries, and regularizes outliers through curvature-based smoothness. We prove that HCDV approximately satisfies the four Shapley axioms with surplus loss O(eta log n), enjoys sub-Gaussian coalition deviation tilde O(1/sqrt{T}), and incurs at most k epsilon_infty regret for top-k selection. Experiments on four benchmarks--tabular, vision, streaming, and a 45M-sample CTR task--plus the OpenDataVal suite show that HCDV lifts accuracy by up to +5 pp, slashes valuation time by up to 100x, and directly supports tasks such as augmentation filtering, low-latency streaming updates, and fair marketplace payouts.