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

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.

💡 Research Summary

The paper “Owen‑based Semantics and Hierarchy‑Aware Explanation (O‑Shap)” tackles a fundamental limitation of Shapley‑based XAI methods—namely, the assumption of feature independence—when applied to structured data such as images. In convolutional neural networks, adjacent pixels are highly correlated and jointly contribute to predictions; treating them as independent players leads to attribution cancellation and misleading explanations. To address this, the authors adopt the Owen value, a hierarchical generalization of the Shapley value that allows group‑level attributions while preserving the original axioms of efficiency and linearity.

A central contribution is the identification of a flaw in existing hierarchical SHAP implementations (axis‑aligned AA‑SHAP and SLIC‑based superpixel SHAP). These methods often violate the T‑property, a consistency condition that requires coarse‑level segments to be unions of finer‑level segments. Without T‑property, the Owen value can produce unstable or semantically incoherent attributions.

The authors therefore propose a novel semantics‑aware segmentation pipeline. First, an edge detector (Canny) creates a coarse layer. Then, a graph‑based merging algorithm iteratively refines the hierarchy, using “attribution‑aware” edge weights derived from a pretrained model’s preliminary explanations. This process is mathematically proven to satisfy the T‑property, ensuring that each higher‑level group is exactly the union of its child groups.

With a valid hierarchy in place, the Owen value is computed as a double expectation: an outer average over all permutations of groups and an inner average over permutations of features within each group. This reduces the naïve exponential cost O(2^|N|) of exact Shapley computation to a polynomial bound O(|N|^2)–O(|N|^3), depending on the hierarchy depth. The paper provides a formal complexity analysis confirming this reduction.

To align the axiomatic foundation with image data, the authors reformulate the Shapley symmetry and dummy axioms into group‑symmetry and group‑dummy axioms, which apply only within semantically coherent groups. They prove that under these four axioms (efficiency, linearity, group‑symmetry, group‑dummy) the Owen value is the unique solution.

Empirical evaluation spans five image datasets (including CIFAR‑10, ImageNet‑subset, and Pascal VOC) and one tabular dataset (Adult Income). O‑Shap is compared against seven SHAP variants (Kernel SHAP, TreeSHAP, Causal SHAP, GraphSHAP, etc.) across five metrics: attribution precision (IoU with ground‑truth masks), semantic coherence (alignment with object boundaries), runtime, user‑study based interpretability, and model‑agnostic stability. Results show that O‑Shap consistently outperforms baselines, achieving 12‑18 % higher precision and markedly better semantic alignment, while reducing computation time by up to 40 % thanks to the hierarchical pruning.

The paper’s contributions can be summarized as: (1) exposing the inadequacy of standard Shapley axioms for vision models and introducing group‑aware axioms; (2) proving the necessity of the T‑property for valid hierarchical segmentations; (3) designing a semantics‑driven, T‑property‑satisfying segmentation algorithm; (4) extending Owen‑value theory to multi‑layer hierarchies with provable polynomial‑time complexity; and (5) delivering extensive empirical evidence of superior explanation quality and efficiency.

Limitations include the linear scaling of the segmentation step with image resolution and the current focus on CNN architectures, leaving Transformer‑based vision models as future work. The authors suggest extending the framework to multimodal data, non‑image graphs, and automating T‑property verification via meta‑learning. Overall, O‑Shap represents a significant step toward theoretically sound, structure‑aware, and computationally feasible XAI for complex, high‑dimensional data.