On the influence of dependent features in classification problems: A game-theoretic perspective

This paper deals with a new measure of the influence of each feature on the outcome 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 outcome. 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. • We propose an influence measure for dependent features on classification problems. • Our measure is axiomatically characterized using cooperative game theory properties. • The introduced influence measure is a generalization of the Banzhaf-Owen value. • We provide a sampling method to approximate the measure in large-scale contexts. • We explore the importance of features in several datasets to validate our proposals.