SHAP is one of the most popular local feature-attribution methods. Given a function f and an input x, it quantifies each feature's contribution to f(x). Recently, SHAP has been increasingly used for global insights: practitioners average the absolute SHAP values over many data points to compute global feature importance scores, which are then used to discard unimportant features. In this work, we investigate the soundness of this practice by asking whether small aggregate SHAP values necessarily imply that the corresponding feature does not affect the function. Unfortunately, the answer is no: even if the i-th SHAP value is 0 on the entire data support, there exist functions that clearly depend on Feature i. The issue is that computing SHAP values involves evaluating f on points outside of the data support, where f can be strategically designed to mask its dependence on Feature i. To address this, we propose to aggregate SHAP values over the extended support, which is the product of the marginals of the underlying distribution. With this modification, we show that a small aggregate SHAP value implies that we can safely discard the corresponding feature. We then extend our results to KernelSHAP, the most popular method to approximate SHAP values in practice. We show that if KernelSHAP is computed over the extended distribution, a small aggregate value justifies feature removal. This result holds independently of whether KernelSHAP accurately approximates true SHAP values, making it one of the first theoretical results to characterize the KernelSHAP algorithm itself. Our findings have both theoretical and practical implications. We introduce the Shapley Lie algebra, which offers algebraic insights that may enable a deeper investigation of SHAP and we show that randomly permuting each column of the data matrix enables safely discarding features based on aggregate SHAP and KernelSHAP values.

翻译：SHAP是最流行的局部特征归因方法之一。给定函数f和输入x，该方法量化每个特征对f(x)的贡献。近年来，SHAP越来越多地被用于全局分析：实践者通过对多个数据点的绝对SHAP值取平均来计算全局特征重要性得分，进而用于舍弃不重要特征。本文通过探究"较小的聚合SHAP值是否必然意味着对应特征不影响函数功能"来检验该实践方法的可靠性。遗憾的是，答案是否定的：即使第i个SHAP值在整个数据支撑集上均为0，仍存在明显依赖于特征i的函数。问题在于SHAP值的计算涉及在数据支撑集之外的点上评估函数f，而f可能被策略性地设计以掩盖其对特征i的依赖性。为解决此问题，我们提出在扩展支撑集上聚合SHAP值，该扩展支撑集是基础分布边缘分布的乘积。通过此修正，我们证明较小的聚合SHAP值意味着可以安全舍弃对应特征。随后我们将结果推广至KernelSHAP——实践中最常用的SHAP值近似计算方法。我们证明若在扩展分布上计算KernelSHAP，较小的聚合值可为特征移除提供依据。该结论独立于KernelSHAP是否准确逼近真实SHAP值，使其成为首个刻画KernelSHAP算法本身的理论成果之一。我们的发现兼具理论与实际意义：通过引入Shapley李代数提供了可能深化SHAP研究的代数视角，并证明对数据矩阵每列进行随机置换可实现基于聚合SHAP值与KernelSHAP值的特征安全舍弃。