Detecting Feature Interactions in Bagged Trees and Random Forests

Additive models remain popular statistical tools due to their ease of interpretation and as a result, hypothesis tests for additivity have been developed to asses the appropriateness of these models. However, as data continues to grow in size and complexity, practicioners are relying more heavily on learning algorithms because of their predictive superiority. Due to the black-box nature of these learning methods, the increase in predictive power is assumed to come at the cost of interpretability and understanding. However, recent work suggests that many popular learning algorithms, such as bagged trees and random forests, have desireable asymptotic properties which allow for formal statistical inference when base learners are built with subsamples. This work extends the hypothesis tests previously developed and demonstrates that by constructing an appropriate test set, we may perform formal hypothesis tests for additivity amongst features. We develop notions of total and partial additivity and demonstrate that both tests can be carried out at no additional computational cost to the original ensemble. Simulations and demonstrations on real data are also provided.