  Low-order functional ANOVA (fANOVA) models have been rediscovered in the
machine learning (ML) community under the guise of inherently interpretable
machine learning. Explainable Boosting Machines or EBM (Lou et al. 2013) and
GAMI-Net (Yang et al. 2021) are two recently proposed ML algorithms for fitting
functional main effects and second-order interactions. We propose a new
algorithm, called GAMI-Tree, that is similar to EBM, but has a number of
features that lead to better performance. It uses model-based trees as base
learners and incorporates a new interaction filtering method that is better at
capturing the underlying interactions. In addition, our iterative training
method converges to a model with better predictive performance, and the
embedded purification ensures that interactions are hierarchically orthogonal
to main effects. The algorithm does not need extensive tuning, and our
implementation is fast and efficient. We use simulated and real datasets to
compare the performance and interpretability of GAMI-Tree with EBM and
GAMI-Net.
