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Recent papers have used machine learning architecture to fit low-orderfunctional ANOVA models with main effects and second-order interactions. TheseGAMI (GAM + Interaction) models are directly interpretable as the functionalmain effects and interactions can be easily plotted and visualized.Unfortunately, it is not easy to incorporate the monotonicity requirement intothe existing GAMI models based on boosted trees, such as EBM (Lou et al. 2013)and GAMI-Lin-T (Hu et al. 2022). This paper considers models of the form$f(x)=\sum_{j,k}f_{j,k}(x_j, x_k)$ and develops monotone tree-based GAMImodels, called monotone GAMI-Tree, by adapting the XGBoost algorithm. It isstraightforward to fit a monotone model to $f(x)$ using the options in XGBoost.However, the fitted model is still a black box. We take a different approach:i) use a filtering technique to determine the important interactions, ii) fit amonotone XGBoost algorithm with the selected interactions, and finally iii)parse and purify the results to get a monotone GAMI model. Simulated datasetsare used to demonstrate the behaviors of mono-GAMI-Tree and EBM, both of whichuse piecewise constant fits. Note that the monotonicity requirement is for thefull model. Under certain situations, the main effects will also be monotone.But, as seen in the examples, the interactions will not be monotone.

Monotone Tree-Based GAMI Models by Adapting XGBoost