论分类问题中相关特征的影响：博弈论视角
On the influence of dependent features in classification problems: a game-theoretic perspective
AI总结：
提出一种考虑特征子集依赖的分类特征影响新度量，并从合作博弈论出发给出公理化刻画，证明其可一般化刻画带先验联盟博弈的 Banzhaf-Owen 值。
摘要：
本文研究一种衡量分类问题中各特征对响应变量影响的新度量，该度量考虑了某些特征子集之间潜在的依赖关系。在此框架下，我们考虑一个由个体组成的样本，每个个体由特定特征刻画，每个特征包含有限的取值范围，并依据二元响应变量进行分类。该度量最终被证明是一种已有文献探讨过的、与合作博弈论相关的影响度量。我们通过将合作博弈论中的性质调整并应用于具体情境，对所提出的影响度量给出了公理化刻画。此外，我们从分类问题的角度证明，该影响度量构成了针对具有先验联盟的博弈中著名的 Banzhaf-Owen 值的一般性刻画。文中给出的定义和结果通过数值示例和多种应用加以说明，为我们的方法提供了实用洞见。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
