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Owen-based Semantics and Hierarchy-Aware Explanation (O-Shap)

Xiangyu Zhou, Chenhan Xiao, Yang Weng

TL;DR

The paper tackles the limitations of SHAP in vision tasks arising from feature dependencies by introducing O-Shap, an Owen-value-based, hierarchy-aware explanation framework. It reformulates Shapley axioms for image data into group-level variants (Group Symmetry and Group Dummy) and extends the Owen value to multi-level hierarchies, enabling structure-aware attributions with polynomial-time complexity $O(|N|^{n \cdot \log_{n}{2}})$ under balanced partitions. A semantics-aware segmentation pipeline is proposed to satisfy the positive $T$-Property, ensuring semantic coherence across hierarchy levels. Extensive experiments on five image datasets and one tabular dataset demonstrate superior attribution precision and runtime efficiency compared to seven SHAP variants, highlighting the method’s robustness when structure matters.

Abstract

Shapley value-based methods have become foundational in explainable artificial intelligence (XAI), offering theoretically grounded feature attributions through cooperative game theory. However, in practice, particularly in vision tasks, the assumption of feature independence breaks down, as features (i.e., pixels) often exhibit strong spatial and semantic dependencies. To address this, modern SHAP implementations now include the Owen value, a hierarchical generalization of the Shapley value that supports group attributions. While the Owen value preserves the foundations of Shapley values, its effectiveness critically depends on how feature groups are defined. We show that commonly used segmentations (e.g., axis-aligned or SLIC) violate key consistency properties, and propose a new segmentation approach that satisfies the $T$-property to ensure semantic alignment across hierarchy levels. This hierarchy enables computational pruning while improving attribution accuracy and interpretability. Experiments on image and tabular datasets demonstrate that O-Shap outperforms baseline SHAP variants in attribution precision, semantic coherence, and runtime efficiency, especially when structure matters.

Owen-based Semantics and Hierarchy-Aware Explanation (O-Shap)

TL;DR

The paper tackles the limitations of SHAP in vision tasks arising from feature dependencies by introducing O-Shap, an Owen-value-based, hierarchy-aware explanation framework. It reformulates Shapley axioms for image data into group-level variants (Group Symmetry and Group Dummy) and extends the Owen value to multi-level hierarchies, enabling structure-aware attributions with polynomial-time complexity under balanced partitions. A semantics-aware segmentation pipeline is proposed to satisfy the positive -Property, ensuring semantic coherence across hierarchy levels. Extensive experiments on five image datasets and one tabular dataset demonstrate superior attribution precision and runtime efficiency compared to seven SHAP variants, highlighting the method’s robustness when structure matters.

Abstract

Shapley value-based methods have become foundational in explainable artificial intelligence (XAI), offering theoretically grounded feature attributions through cooperative game theory. However, in practice, particularly in vision tasks, the assumption of feature independence breaks down, as features (i.e., pixels) often exhibit strong spatial and semantic dependencies. To address this, modern SHAP implementations now include the Owen value, a hierarchical generalization of the Shapley value that supports group attributions. While the Owen value preserves the foundations of Shapley values, its effectiveness critically depends on how feature groups are defined. We show that commonly used segmentations (e.g., axis-aligned or SLIC) violate key consistency properties, and propose a new segmentation approach that satisfies the -property to ensure semantic alignment across hierarchy levels. This hierarchy enables computational pruning while improving attribution accuracy and interpretability. Experiments on image and tabular datasets demonstrate that O-Shap outperforms baseline SHAP variants in attribution precision, semantic coherence, and runtime efficiency, especially when structure matters.
Paper Structure (15 sections, 5 theorems, 4 equations, 8 figures, 3 tables, 1 algorithm)

This paper contains 15 sections, 5 theorems, 4 equations, 8 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methods
  4. Notations and Shapley Value-Based XAI Method
  5. Reformulating Axioms for Image Data: Owen Value
  6. Owen Value under Multi-Layer Hierarchy
  7. A Semantics-Aware Segmentation
  8. Experiments
  9. Evaluating the Limitations of Shapley-Based Attribution
  10. Evaluating the Role of Segmentation in O-Shap
  11. Comprehension Comparison among Many Baselines on Various Image Dataset
  12. Evaluation on Execution Time
  13. Sensitivity Study of Hyperparameters of Segmentation
  14. Evaluation on Non-image Dataset
  15. Conclusion

Key Result

Proposition 1

Let $\bm{x} \in \mathcal{X} = \{x_1, \cdots, x_i, \cdots, |N|\}$ denote the input image, $N=\{1,\cdots,i,\cdots,|N|\}$ denote the feature set, and let $f: \mathcal{X} \to \mathbb{R}$ be the model. The Shapley value $\varphi$ in Eq. (eq:Shapleyvalue) is the unique attribution satisfying the following

Figures (8)

  • Figure 1: Overview of the motivation (a), design (b), and preliminary result (c) of O-Shap.
  • Figure 2: Example of the hierarchical structure of an image.
  • Figure 3: Limitation of SHAP and a hierarchy-aware solution.
  • Figure 4: Explanation heatmaps under various segmentations.
  • Figure 5: Explanations in ImageNet-S50 with mIoU scores.
  • ...and 3 more figures

Theorems & Definitions (9)

  • Proposition 1: Axiomatic Characterization of the Shapley Value
  • Proposition 2: Uniqueness of the Owen Value under Group-Aware Axioms
  • Proposition 3: Computational Efficiency
  • proof
  • Definition 1: Positive $\mathcal{T}$-Property
  • Proposition 4
  • proof
  • Proposition 5: Satisfaction of the $\mathcal{T}$-Property
  • proof