arXiv:2602.22882cs.LG2026-02

多输出模型的特征归因必须分输出独立计算,否则无法保证公平性。

Fair feature attribution for multi-output prediction: a Shapley-based perspective

  • 基于博弈论的谢尔普利值框架,推导出多输出归因的理论约束
  • 实验表明多输出模型可节省训练与部署开销,同时保持解释一致性
  • 适用于需公平解释的生物医学等多输出预测场景

本文在谢尔普利值框架下,对多输出预测模型的特征归因进行了公理化分析。尽管现有方法对每个输出独立计算SHAP值,但其理论必要性长期未明。通过将经典谢尔普利公理扩展至向量值合作博弈,我们证明了一个刚性定理:任何满足效率、对称性、虚拟玩家和可加性的归因规则,必然在输出维度上分量分解。因此,联合输出的归因规则必须放松至少一个经典公理。该结果揭示了谢尔普利基可解释性中此前未形式化的结构性约束,明确了公平一致解释在多输出学习中的精确范围。在生物医学基准上的数值实验表明,多输出模型在训练与部署中可实现计算节约,同时生成的SHAP解释仍完全符合谢尔普利公理所要求的分量结构。

原文摘要 · Abstract (English)

In this article, we provide an axiomatic characterization of feature attribution for multi-output predictors within the Shapley framework. While SHAP explanations are routinely computed independently for each output coordinate, the theoretical necessity of this practice has remained unclear. By extending the classical Shapley axioms to vector-valued cooperative games, we establish a rigidity theorem showing that any attribution rule satisfying efficiency, symmetry, dummy player, and additivity must necessarily decompose component-wise across outputs. Consequently, any joint-output attribution rule must relax at least one of the classical Shapley axioms. This result identifies a previously unformalized structural constraint in Shapley-based interpretability, clarifying the precise scope of fairness-consistent explanations in multi-output learning. Numerical experiments on a biomedical benchmark illustrate that multi-output models can yield computational savings in training and deployment, while producing SHAP explanations that remain fully consistent with the component-wise structure imposed by the Shapley axioms.

特征归因多输出谢尔普利值公平性

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