Monotone Tree-Based GAMI Models by Adapting XGBoost
This work addresses the need for interpretable machine learning models with monotonicity constraints, which is important for domains requiring transparent and reliable predictions, though it is incremental as it builds on existing GAMI and XGBoost frameworks.
The paper tackles the challenge of incorporating monotonicity constraints into interpretable GAMI models by developing monotone GAMI-Tree, which adapts XGBoost to fit models with main effects and interactions while ensuring monotonicity, and demonstrates its behavior on simulated datasets compared to existing methods like EBM.
Recent papers have used machine learning architecture to fit low-order functional ANOVA models with main effects and second-order interactions. These GAMI (GAM + Interaction) models are directly interpretable as the functional main effects and interactions can be easily plotted and visualized. Unfortunately, it is not easy to incorporate the monotonicity requirement into the 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 GAMI models, called monotone GAMI-Tree, by adapting the XGBoost algorithm. It is straightforward 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 a monotone XGBoost algorithm with the selected interactions, and finally iii) parse and purify the results to get a monotone GAMI model. Simulated datasets are used to demonstrate the behaviors of mono-GAMI-Tree and EBM, both of which use piecewise constant fits. Note that the monotonicity requirement is for the full model. Under certain situations, the main effects will also be monotone. But, as seen in the examples, the interactions will not be monotone.