This research presents Gradient Boosted Tree High Importance Path Snippets (gbt-HIPS), a novel, heuristic method for explaining gradient boosted tree (GBT) classification models by extracting a single classification rule (CR) from the ensemble of decision trees that make up the GBT model. This CR contains the most statistically important boundary values of the input space as antecedent terms. The CR represents a hyper-rectangle of the input space inside which the GBT model is, very reliably, classifying all instances with the same class label as the explanandum instance. In a benchmark test using nine data sets and five competing state-of-the-art methods, gbt-HIPS offered the best trade-off between coverage (0.16–0.75) and precision (0.85–0.98). Unlike competing methods, gbt-HIPS is also demonstrably guarded against under- and over-fitting. A further distinguishing feature of our method is that, unlike much prior work, our explanations also provide counterfactual detail in accordance with widely accepted recommendations for what makes a good explanation.
Regularity ofC1and Lipschitz domains in terms of the Beurling transform
