用随机矩阵理论诊断交通碰撞模型过拟合，发现谱指数α可预测专家判断。
Beyond Accuracy: A Unified Random Matrix Theory Diagnostic Framework for Crash Classification Models
- 基于随机矩阵理论与重尾自正则化，构建覆盖多种模型的谱诊断框架。
- 良好正则化的模型谱指数α稳定在[2,4]区间（均值2.87±0.34），过拟合则α<2或谱坍塌。
- α与专家共识高度相关（斯皮尔曼ρ=0.89），适合用于模型早期停止与选择。
交通碰撞分类模型通常以准确率、F1或AUC评估，但这些指标无法揭示模型是否隐性过拟合。本文提出一种基于随机矩阵理论（RMT）与重尾自正则化（HTSR）的谱诊断框架，涵盖BERT/ALBERT/Qwen2.5的权重矩阵、XGBoost/随机森林的交叉验证增量矩阵、逻辑回归的实证海森矩阵、决策树的诱导亲和矩阵以及KNN的图拉普拉斯矩阵。在两个爱荷华州交通局（Iowa DOT）的碰撞分类任务上（分别含173,512与371,062条记录）评估九类模型，发现幂律指数α提供结构质量信号：正则良好的模型α稳定在[2,4]区间（均值2.87±0.34），而过拟合模型则表现为α<2或谱坍塌。α与专家共识存在强秩相关性（斯皮尔曼ρ=0.89，p<0.001），表明谱质量能捕捉与专家推理一致的模型行为。本文提出基于α的早停准则与谱模型选择协议，并在交叉验证F1基准上验证其有效性。稀疏Lanczos近似使该框架可扩展至大规模数据集。
原文摘要 · Abstract (English)
Crash classification models in transportation safety are typically evaluated using accuracy, F1, or AUC, metrics that cannot reveal whether a model is silently overfitting. We introduce a spectral diagnostic framework grounded in Random Matrix Theory (RMT) and Heavy-Tailed Self-Regularization (HTSR) that spans the ML taxonomy: weight matrices for BERT/ALBERT/Qwen2.5, out-of-fold increment matrices for XGBoost/Random Forest, empirical Hessians for Logistic Regression, induced affinity matrices for Decision Trees, and Graph Laplacians for KNN. Evaluating nine model families on two Iowa DOT crash classification tasks (173,512 and 371,062 records respectively), we find that the power-law exponent $α$ provides a structural quality signal: well-regularized models consistently yield $α$ within $[2, 4]$ (mean $2.87 \pm 0.34$), while overfit variants show $α< 2$ or spectral collapse. We observe a strong rank correlation between $α$ and expert agreement (Spearman $ρ= 0.89$, $p < 0.001$), suggesting spectral quality captures model behaviors aligned with expert reasoning. We propose an $α$-based early stopping criterion and a spectral model selection protocol, and validate both against cross-validated F1 baselines. Sparse Lanczos approximations make the framework scalable to large datasets.
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