pureGAM: Learning an Inherently Pure Additive Model

Including pairwise or higher-order interactions among predictors of a Generalized Additive Model (GAM) is gaining increasing attention in the literature. However, existing models face an identifiability challenge. In this paper, we propose pureGAM, an inherently pure additive model of both main effects and higher-order interactions. By imposing the pureness condition to constrain each component function, pureGAM is proved to be identifiable without compromising accuracy. Furthermore, the pureness condition introduces additional interpretability in terms of simplicity. Practically, pureGAM is a unified model to support both numerical and categorical features with a novel learning procedure to achieve optimal performance. Evaluations show that pureGAM outperforms other GAMs and has very competitive performance even compared with opaque models, and its interpretability remarkably outperforms competitors in terms of pureness. We also share a successful adoption of pureGAM in one real-world application.