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

Canran Xiao, Jiabao Dou, Zhiming Lin, Zong Ke, Liwei Hou

TL;DR

This work addresses the computational bottleneck and geometry-insensitivity of classical data Shapley valuation by introducing Hierarchical Contrastive Data Valuation (HCDV). HCDV combines a geometry-preserving contrastive embedding with a coarse-to-fine hierarchical partition of the data and local Shapley computations that propagate budgets downward, achieving scalable, multiscale data valuation. The authors provide theoretical guarantees on approximate Shapley properties, concentration, and top-k surrogate regret, and demonstrate substantial accuracy gains, runtime reductions, and practical benefits in augmentation filtering, streaming updates, and data marketplace pricing across diverse benchmarks. The approach enables geometry-aware, scalable, and interpretable data valuation with strong empirical and theoretical support for real-world data-centric ML systems.

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.

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

TL;DR

This work addresses the computational bottleneck and geometry-insensitivity of classical data Shapley valuation by introducing Hierarchical Contrastive Data Valuation (HCDV). HCDV combines a geometry-preserving contrastive embedding with a coarse-to-fine hierarchical partition of the data and local Shapley computations that propagate budgets downward, achieving scalable, multiscale data valuation. The authors provide theoretical guarantees on approximate Shapley properties, concentration, and top-k surrogate regret, and demonstrate substantial accuracy gains, runtime reductions, and practical benefits in augmentation filtering, streaming updates, and data marketplace pricing across diverse benchmarks. The approach enables geometry-aware, scalable, and interpretable data valuation with strong empirical and theoretical support for real-world data-centric ML systems.

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.
Paper Structure (90 sections, 7 theorems, 63 equations, 3 figures, 5 tables, 2 algorithms)

This paper contains 90 sections, 7 theorems, 63 equations, 3 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Data Valuation Framework
  4. Canonical Axioms for Data Valuation
  5. Efficiency (Completeness).
  6. Symmetry (Fairness).
  7. Dummy Player.
  8. Additivity.
  9. Hierarchical Contrastive Data Valuation
  10. Stage I: Geometry-Preserving Representation
  11. Embedding model.
  12. Embedding objective.
  13. Stage II: Hierarchical Decomposition
  14. Recursive clustering.
  15. Stage III: Multi‑Resolution Shapley Attribution
  16. ...and 75 more sections

Key Result

Theorem 1

For HCDV with $L$ levels and budget propagation (Eq. eq:234 and the corresponding normalised weights), In particular, if $|G|\le M$ for all leaves, then $\varepsilon_{\mathrm{leaf}}=0$.

Figures (3)

  • Figure 1: Effect of adding 1k augmented samples selected by different method. 'Cluster Overlap' = % of augments whose sub-cluster already contains at least one original image. Better sample efficiency: higher accuracy, lower overlap.
  • Figure 2: Class coverage of selected augmentations (number of unique classes represented). Higher is better.
  • Figure 3: Streaming valuation on click-stream benchmark.

Theorems & Definitions (15)

  • Definition 1: Data Valuation Function
  • Theorem 1: Global efficiency
  • Proposition 1: Coalition-level deviation
  • Theorem 2: Regret for top--$k$ under surrogate utility
  • proof : Proof of Theorem \ref{['thm:efficiency']}
  • Lemma 1: Unbiasedness of the permutation estimator
  • proof
  • proof : Proof of Proposition \ref{['prop:concentration']}
  • proof : Proof of Theorem \ref{['thm:regret']}
  • Proposition 2: Approximate symmetry and dummy (coalition level)
  • ...and 5 more