arXiv:2605.19618cs.LGstat.ME2026-05

提出新评估框架,精准定位可解释树模型重构失败原因。

A Family of Divergence Measures for Evaluating the Reconstruction Quality of Explainable Ensemble Trees

论文配图:A Family of Divergence Measures for Evaluating the Reconstruction Quality of Explainable Ensemble Trees
图 1 · 摘自论文原文
  • 基于nLoI统计框架,分解节点内与节点间误差
  • 四类互补指标可检测相关性忽略的结构偏差
  • 适用于可解释集成树模型,适合算法验证者

为验证集成学习器的可解释代理模型,需衡量其内部表示与代理近似之间的一致性,而非仅相关性。传统相关性方法因尺度不变性,无法发现共现结构中的系统性差异。本文提出以标准化解释损失(nLoI)为核心的统计框架,基于Cressie-Read幂发散族(λ=2),可闭式分解为节点内与节点间成分,实现对重构失败位置与原因的精准诊断。框架包含四个互补度量,分别捕捉近似质量的不同结构特征。统一的置换检验程序可在一次重采样中完成所有度量的有效推断。理论证明各度量具有有界性和对称性。蒙特卡洛模拟与实证评估表明,该框架严格控制第一类错误,并能检测出相关性方法无法察觉的重构保真度梯度。框架在可解释集成树(E2Tree)背景下开发并验证,基于三个基准数据集的实验展示了其实际应用价值。

原文摘要 · Abstract (English)

Validating interpretable surrogate models for ensemble learners requires measuring agreement between the ensemble's internal representation and its surrogate approximation, rather than mere association. Correlation-based approaches are scale-invariant and fail to detect systematic discrepancies in co-occurrence structure. We propose a statistical framework grounded in the agreement-association distinction, centered on the normalized Loss of Interpretability (nLoI). Rooted in the Cressie-Read power divergence family with lambda equal to 2, the nLoI admits a closed-form decomposition into within-node and between-node components, providing a unique diagnostic capability to identify precisely where and why reconstruction fails. The framework incorporates four complementary measures capturing distinct structural facets of approximation quality. A unified permutation testing procedure delivers valid inference for all measures within a single resampling pass. Theoretical properties, including boundedness and symmetry, are established for each metric. Monte Carlo simulations and empirical evaluations confirm exact Type I error control and demonstrate that these measures detect reconstruction fidelity gradients invisible to correlation-based alternatives. The framework is developed and illustrated in the context of Explainable Ensemble Trees (E2Tree), and empirical evaluation on three benchmark datasets illustrates the practical utility of the framework.

可解释性模型评估集成学习统计检验

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