This paper deals with a new measure of the influence of each feature on the response variable in classification problems, accounting for potential dependencies among certain feature subsets. Within this framework, we consider a sample of individuals characterized by specific features, each feature encompassing a finite range of values, and classified based on a binary response variable. This measure turns out to be an influence measure explored in existing literature and related to cooperative game theory. We provide an axiomatic characterization of our proposed influence measure by tailoring properties from the cooperative game theory to our specific context. Furthermore, we demonstrate that our influence measure becomes a general characterization of the well-known Banzhaf-Owen value for games with a priori unions, from the perspective of classification problems. The definitions and results presented herein are illustrated through numerical examples and various applications, offering practical insights into our methodologies.

翻译：本文提出了一种新的度量方法，用于衡量分类问题中每个特征对响应变量的影响，同时考虑特定特征子集间可能存在的依赖关系。在此框架下，我们考虑一个由特定特征描述的个体样本，每个特征具有有限取值范围，并基于二元响应变量进行分类。该度量方法被证明是现有文献中已探讨的一种影响度量，并与合作博弈论相关。我们通过将合作博弈论的性质适配到具体分类情境，为所提出的影响度量提供了公理化表征。此外，我们证明从分类问题的视角来看，该影响度量可视为具有先验联盟的博弈中著名的班扎夫-欧文值的一般化表征。本文通过数值算例与多种应用场景对所提出的定义与结论进行了阐释，为相关方法论提供了实践参考。