量化了信用风险模型中单调性约束带来的精度损失，发现大数据下几乎无代价。
What's the Price of Monotonicity? A Multi-Dataset Benchmark of Monotone-Constrained Gradient Boosting for Credit PD
- 在五个公开数据集上对比有无单调性约束的梯度提升模型
- 小数据集上精度损失可达2-3%，大数据集上不足0.2%
- 适合关注可解释性的金融风控从业者参考
金融机构在部署信用风险机器学习模型时面临预测精度与可解释性之间的权衡。单调性约束使模型行为符合领域知识，但其性能代价——即单调性成本——尚未被充分量化。本文在五个公开数据集和三个库上，对信用违约概率建模中的单调约束与非约束梯度提升模型进行基准测试。我们定义单调性成本（PoM）为从无约束模型转向约束模型时标准评估指标的相对变化，通过配对比较与自助法估计不确定性。实验显示，AUC上的PoM范围从几乎为零到约2.9%：在大规模数据集上几乎无成本（通常低于0.2%，常不可区分），而在小数据集且约束覆盖广泛时最昂贵（约2-3%）。因此，合理设定的单调性约束通常可在保持较小精度损失的前提下实现可解释性，尤其适用于大规模信用组合场景。
原文摘要 · Abstract (English)
Financial institutions face a trade-off between predictive accuracy and interpretability when deploying machine learning models for credit risk. Monotonicity constraints align model behavior with domain knowledge, but their performance cost - the price of monotonicity - is not well quantified. This paper benchmarks monotone-constrained versus unconstrained gradient boosting models for credit probability of default across five public datasets and three libraries. We define the Price of Monotonicity (PoM) as the relative change in standard performance metrics when moving from unconstrained to constrained models, estimated via paired comparisons with bootstrap uncertainty. In our experiments, PoM in AUC ranges from essentially zero to about 2.9 percent: constraints are almost costless on large datasets (typically less than 0.2 percent, often indistinguishable from zero) and most costly on smaller datasets with extensive constraint coverage (around 2-3 percent). Thus, appropriately specified monotonicity constraints can often deliver interpretability with small accuracy losses, particularly in large-scale credit portfolios.
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