将梯度提升树的叶值视为坐标，实现精确的对比解释。
Leaf Values as Coordinates: Exact Contrastive Explanation for Gradient-Boosted Ensembles
- 把每棵树的叶值看作空间坐标，模型决策变为线性运算。
- 对比解释精确到10^-15，可复现模型决策过程。
- 推荐方案真实可行，适合需要可执行解释的场景。
梯度提升集成模型通过每棵树贡献一个叶值并求和进行预测。若将这些叶值视为坐标而非中间结果，每个样本即成为R^M空间中的点，模型在此空间中线性作用：得分即为坐标的和。这一视角转换使对比解释变得精确。两个样本之间的差异向量在共享叶节点的位置恒为零，因此拒签与通过申请者的差距仅由少数可追溯至真实树分裂的坐标承载。无需拟合、采样或假设特征可加性——可加性早已存在于正确空间中。基于此表示，我们构建了一种可追溯的补救方法，在五个表格数据集上重复交叉验证。其推荐结果可精确重建模型自身决策至6.2×10^-15水平，审计者可无需模型直接复核计算。在信用数据集上，该方法在努力成本与真实性之间达到帕累托非支配状态。当限制推荐变化为个体实际可改变项（如年龄、既定违约）时，仍保持58%有效性，而最强基线仅41%，标准评估因未考察可行性而无法识别此差异。
原文摘要 · Abstract (English)
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.
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