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Precedence-Constrained Winter Value for Effective Graph Data Valuation

Hongliang Chi, Wei Jin, Charu Aggarwal, Yao Ma

TL;DR

Graph data valuation must account for inter-node dependencies and unlabeled elements, which challenge traditional i.i.d.-based methods like Data Shapley. We introduce PC-Winter, a precedence-constrained Winter value defined on a computation-tree-based contribution structure that captures hierarchical, unilateral dependencies among graph elements. The method uses DFS-generated permissible permutations and three efficiency techniques—permutation sampling, hierarchical truncation, and local propagation—to enable streaming estimation of per-player values $\psi_p(\mathcal{P}, U)$ and subsequent node/edge valuations. Empirical results on six real-world graphs show PC-Winter consistently outperforms Data Shapley in identifying high-value nodes and edges while offering substantial computational speedups, underscoring its practical utility for graph data monetization and model-training guidance. Future work includes scaling further and extending PC-Winter to heterogeneous graphs, broadening its applicability across graph-centric domains.

Abstract

Data valuation is essential for quantifying data's worth, aiding in assessing data quality and determining fair compensation. While existing data valuation methods have proven effective in evaluating the value of Euclidean data, they face limitations when applied to the increasingly popular graph-structured data. Particularly, graph data valuation introduces unique challenges, primarily stemming from the intricate dependencies among nodes and the exponential growth in value estimation costs. To address the challenging problem of graph data valuation, we put forth an innovative solution, Precedence-Constrained Winter (PC-Winter) Value, to account for the complex graph structure. Furthermore, we develop a variety of strategies to address the computational challenges and enable efficient approximation of PC-Winter. Extensive experiments demonstrate the effectiveness of PC-Winter across diverse datasets and tasks.

Precedence-Constrained Winter Value for Effective Graph Data Valuation

TL;DR

Graph data valuation must account for inter-node dependencies and unlabeled elements, which challenge traditional i.i.d.-based methods like Data Shapley. We introduce PC-Winter, a precedence-constrained Winter value defined on a computation-tree-based contribution structure that captures hierarchical, unilateral dependencies among graph elements. The method uses DFS-generated permissible permutations and three efficiency techniques—permutation sampling, hierarchical truncation, and local propagation—to enable streaming estimation of per-player values and subsequent node/edge valuations. Empirical results on six real-world graphs show PC-Winter consistently outperforms Data Shapley in identifying high-value nodes and edges while offering substantial computational speedups, underscoring its practical utility for graph data monetization and model-training guidance. Future work includes scaling further and extending PC-Winter to heterogeneous graphs, broadening its applicability across graph-centric domains.

Abstract

Data valuation is essential for quantifying data's worth, aiding in assessing data quality and determining fair compensation. While existing data valuation methods have proven effective in evaluating the value of Euclidean data, they face limitations when applied to the increasingly popular graph-structured data. Particularly, graph data valuation introduces unique challenges, primarily stemming from the intricate dependencies among nodes and the exponential growth in value estimation costs. To address the challenging problem of graph data valuation, we put forth an innovative solution, Precedence-Constrained Winter (PC-Winter) Value, to account for the complex graph structure. Furthermore, we develop a variety of strategies to address the computational challenges and enable efficient approximation of PC-Winter. Extensive experiments demonstrate the effectiveness of PC-Winter across diverse datasets and tasks.
Paper Structure (38 sections, 4 theorems, 8 equations, 12 figures, 5 tables)

This paper contains 38 sections, 4 theorems, 8 equations, 12 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Preliminary and Related Work
  3. Cooperative Game Theory
  4. Data Valuation and Data Shapley
  5. Graphs and Graph Neural Networks
  6. Methodology
  7. The Graph Data Valuation Problem
  8. Precedence-Constrained Winter Value
  9. Permissible Permutations for PC-Winter
  10. Efficient Approximation of PC-Winter
  11. From PC-Winter to Node and Edge Values
  12. Experiment
  13. Overall Experimental Setup
  14. Dropping High-Value Nodes
  15. Adding High-Value Edges
  16. ...and 23 more sections

Key Result

Theorem 1

Given a contribution tree $\mathcal{T}$ with a set of players $\mathcal{P}$, any DFS traversal over the $\mathcal{T}$ results in a permissible permutation of $\mathcal{P}$ that satisfies both the Level Constraint and Precedence Constraint.

Figures (12)

  • Figure 1: Level Coalition Structure
  • Figure 2: The Structure of a Graph Data Valuation Game
  • Figure 3: Dropping High-value Nodes
  • Figure 4: Adding the High-valued Edges
  • Figure 5: Ablation Study
  • ...and 7 more figures

Theorems & Definitions (9)

  • Definition 1: Computation Tree
  • Definition 2: Player Set
  • Definition 3: Utility Function
  • Theorem 1: Specificity
  • Theorem 2: Exhaustiveness
  • Theorem 1: Specificity
  • proof
  • Theorem 2: Exhaustiveness
  • proof