为可解释提升机提供快速统计推断，实现特征重要性量化。
Statistical Inference for Explainable Boosting Machines
- 用移动平均替代树的累加，使提升过程收敛到特征核岭回归。
- 预测误差达最优速率 $O(p n^{-2/3})$，突破高维困境。
- 计算高效，支持响应值预测区间与特征函数置信区间生成。
可解释提升机（EBM）是流行的“透明盒子”模型，通过提升树学习一组单变量函数，并以可视化方式呈现各特征的影响。然而，与线性模型系数不同，其学习函数的不确定性量化需依赖计算昂贵的自助法，难以判断特征实际重要性。本文利用梯度提升的最新统计推断进展，提出替代方法并提供端到端理论保证。采用移动平均代替树的和（即布洛瓦大道正则化），使提升过程收敛至特征级核岭回归，得到渐近正态的预测结果，对拟合满足Lipschitz条件的广义可加模型（GAM），均方误差达到最小极大最优率 $O(p n^{-2/3})$，成功避免维度灾难。进而构建响应值的预测区间及每个学习函数的置信区间，运行时间与数据点数量无关，显著增强模型可解释性。代码已开源：https://github.com/hetankevin/ebm-inference。
原文摘要 · Abstract (English)
Explainable boosting machines (EBMs) are popular "glass-box" models that learn a set of univariate functions using boosting trees. These achieve explainability through visualizations of each feature's effect. However, unlike linear model coefficients, uncertainty quantification for the learned univariate functions requires computationally intensive bootstrapping, making it hard to know which features truly matter. We provide an alternative using recent advances in statistical inference for gradient boosting, deriving methods for statistical inference as well as end-to-end theoretical guarantees. Using a moving average instead of a sum of trees (Boulevard regularization) allows the boosting process to converge to a feature-wise kernel ridge regression. This produces asymptotically normal predictions that achieve the minimax-optimal MSE for fitting Lipschitz GAMs with $p$ features of $O(p n^{-2/3})$, successfully avoiding the curse of dimensionality. We then construct prediction intervals for the response and confidence intervals for each learned univariate function with a runtime independent of the number of datapoints, enabling further explainability within EBMs. Code is available at https://github.com/hetankevin/ebm-inference.
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