The ubiquitous use of Shapley values in eXplainable AI (XAI) has been triggered by the tool SHAP, and as a result are commonly referred to as SHAP scores. Recent work devised examples of machine learning (ML) classifiers for which the computed SHAP scores are thoroughly unsatisfactory, by allowing human decision-makers to be misled. Nevertheless, such examples could be perceived as somewhat artificial, since the selected classes must be interpreted as numeric. Furthermore, it was unclear how general were the issues identified with SHAP scores. This paper answers these criticisms. First, the paper shows that for Boolean classifiers there are arbitrarily many examples for which the SHAP scores must be deemed unsatisfactory. Second, the paper shows that the issues with SHAP scores are also observed in the case of regression models. In addition, the paper studies the class of regression models that respect Lipschitz continuity, a measure of a function's rate of change that finds important recent uses in ML, including model robustness. Concretely, the paper shows that the issues with SHAP scores occur even for regression models that respect Lipschitz continuity. Finally, the paper shows that the same issues are guaranteed to exist for arbitrarily differentiable regression models.

翻译：在可解释人工智能（XAI）领域，Shapley值的广泛应用由SHAP工具所引发，因此通常被称为SHAP分数。近期研究构建了一些机器学习（ML）分类器的示例，其中计算得到的SHAP分数完全无法令人满意，甚至可能导致人类决策者被误导。然而，这些示例可能被视为具有一定人为性，因为所选类别必须被解释为数值。此外，SHAP分数存在问题的普遍程度尚不明确。本文回应了这些质疑。首先，本文证明对于布尔分类器，存在任意多个SHAP分数必须被视为不满足要求的示例。其次，本文表明SHAP分数的问题在回归模型中同样存在。此外，本文研究了满足Lipschitz连续性的回归模型类别——该函数变化率的度量在机器学习领域具有重要应用，包括模型鲁棒性。具体而言，本文证明即使对于满足Lipschitz连续性的回归模型，SHAP分数的问题仍然会出现。最后，本文论证了相同问题在任意可微回归模型中必然存在。