Leaf Values as Coordinates: Exact Contrastive Explanation for Gradient-Boosted Ensembles
2026-08-19 • Machine Learning
Machine LearningArtificial IntelligenceComputers and Society
AI summaryⓘ
The authors show that by viewing each tree in a gradient-boosted model as producing coordinate values in a space, the model's prediction becomes a simple sum of those coordinates. This makes it easy to explain differences between decisions exactly, since only coordinates from differing tree leaves matter. They use this insight to create a method that suggests changes to achieve a desired outcome, and test it on several datasets. Their method closely matches the model's decisions and makes practical, realistic change recommendations better than existing methods.
gradient boostingensemble learningleaf valuesmodel explanationcontrastive explanationrecourse methodstabular datasetsPareto optimalitycross-validationfeature additivity
Authors
Emanuele Luzio
Abstract
A gradient-boosted ensemble predicts by summing one leaf value per tree. Read those values as coordinates rather than as intermediate results, and every instance becomes a point in R^M on which the model acts linearly: the score is the sum of the coordinates. This small change of view makes contrastive explanation exact. The difference between two instances is a vector that is identically zero wherever they share a leaf, so the gap between a rejected applicant and an accepted one is carried by a handful of coordinates, each traceable to a real split in a real tree. Nothing is fitted, sampled, or assumed additive in features -- the additivity is already there, in the right space. We build a recourse method on this representation and evaluate it on five tabular datasets under repeated cross-validation. Its recommendation reconstructs the model's own decision to 6.2 x 10^-15, so an auditor can re-check the arithmetic without the model. On the credit datasets it is Pareto-non-dominated on effort against realism. And when recommendations are restricted to changes the subject could actually make -- not their age, not a settled delinquency -- it retains 58% of its validity where the strongest baseline retains 41%, a distinction the standard evaluation cannot see because it never asks whether a recommendation can be carried out.