  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.
