Reluctant Interaction Modeling in Generalized Linear Models

Including pairwise interactions in regression models can provide a more accurate approximation of the response surface. However, fitting such models remains particularly challenging in high-dimensional settings, where the number of interactions can reach millions or even billions. Although several methods have been proposed to address this issue, they typically rely on the hierarchical assumption or focus solely on linear models with interactions. In practice, these assumptions are frequently violated. In this paper, we introduce a flexible interaction modeling framework for generalized linear models that does not require the hierarchical assumption. Our approach extends the principle of interaction reluctance to generalized linear models, prioritizing main effects over interactions when their predictive contributions are similar. The method is easy to implement and scales well to very large datasets. We provide finite-sample guarantees for selection consistency in high-dimensional regimes. Numerical studies on simulated data and a real dataset demonstrate that our method achieves strong computational efficiency and favorable statistical performance.