A Monotonicity-Constrained Variable Selection Algorithm for the Inclusion-Exclusion Integral Model: Proposal and Implementation

Abstract

The inclusion-exclusion integral (IE) model is a regression framework based on non-additive measures, designed to explicitly capture interaction effects among explanatory variables while maintaining interpretability. In this study, we address the problem of variable selection under the monotonicity constraint imposed by the fuzzy measure underlying the IE model. To prevent overfitting while preserving meaningful interaction structures, we propose a stepwise variable selection algorithm that explicitly enforces monotonicity constraints. Additionally, to enhance the normality of the response variable and potentially improve model performance, we incorporate the Box-Cox transformation as an optional pre-processing step. Our algorithm adaptively determines whether transformation is beneficial based on data characteristics. Experimental results on benchmark datasets validate the effectiveness of our approach. The implementation is publicly available on GitHub.