Using Model-Based Trees with Boosting to Fit Low-Order Functional ANOVA Models

Interpretability of machine learning (ML) algorithms has been the subject of considerable discussion in recent years. Early approaches relied on post hoc techniques, including variable importance (Breiman 1996), partial dependence plots or PDPs (Friedman 2001), and H-statistics (Friedman and Popescu 2008). These are low-dimensional summaries of high-dimensional models with complex structure, and hence can be inadequate in capturing the full picture. A second approach for model interpretability is the use of surrogate models (or distillation techniques) that fit simpler models to extract information and explanations from the original complex models. Examples include: i) LIME (Ribeiro et al. 2016) based on linear models for local explanations; and ii) locally additive trees for global explanation (Hu et al. 2022). A more recent direction is the use of ML algorithms to fit so-called inherently interpretable models that are extensions of the popular generalized additive models (GAMs) to incorporate common types of interactions. The rationale goes as follows. While there are applications (typically large-scale pattern recognition problems) where the use of very complex algorithms yields new results and insights, in many other areas, nonparametric models with lower-order interactions are sufficient in capturing the structure. This philosophy is a reversal of the trend towards fitting very complex ML models to squeeze out as much predictive performance as possible.