Leaf Values as Coordinates: Exact Contrastive Explanation for Gradient-Boosted Ensembles

Forum topic · 小凯 · 2026-08-21

Summary

This arXiv paper (2608.19127) by Emanuele Luzio introduces a new perspective on interpreting gradient-boosted tree ensembles. By reading each tree's leaf value as a coordinate rather than an intermediate result, every instance becomes a point in R^M on which the model acts linearly—the prediction score is simply the sum of coordinates. This view makes contrastive explanation exact: the difference between two instances is a vector that is identically zero wherever they share leaves, so the gap between a rejected and an accepted applicant is carried by a small set of coordinates, each traceable to a real split in a real tree. No fitting, sampling, or feature-additivity assumptions are required. The authors build a recourse method on this representation and evaluate it on five tabular datasets under repeated cross-validation. The suggested recourses reconstruct the model's own decisions to within 6.2 x 10^-15, enabling auditors to recheck the arithmetic without the model. On a credit dataset, the method is Pareto-nondominated in the effort-plausibility tradeoff. When recourses are restricted to changes an applicant can actually make, it retains 58% effectiveness versus 41% for the strongest baseline—a distinction standard evaluation misses because it never asks whether recourses are actionable.

Paper Overview

Field: Machine Learning Author: Emanuele Luzio Published: 2026-08-19 arXiv: 2608.19127

Introduction

A gradient-boosted ensemble predicts by summing one leaf value per tree. This paper proposes reading those values as coordinates rather than as intermediate results. Under this view, every instance becomes a point in R^M on which the model acts linearly: the score is the sum of the coordinates.

Key Idea

This small change of perspective makes contrastive explanation exact:

The difference between two instances is a vector that is identically zero wherever they share a leaf.
The gap between a rejected applicant and an accepted one is therefore 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.

Recourse Method and Evaluation

The authors build a recourse method on this coordinate representation and evaluate it on five tabular datasets under repeated cross-validation:

Suggested recourses reconstruct the model's own decisions to 6.2 x 10^-15, so auditors can recheck the arithmetic without access to the model.
On a credit dataset, the method is Pareto-nondominated in the effort–plausibility tradeoff.
When recourses are restricted to changes a subject can actually make (not their age, not resolved delinquencies), it retains 58% effectiveness, while the strongest baseline retains 41%. Standard evaluation cannot see this distinction because it never asks whether recourses are executable.