共形分位数回归的非渐近误差界与协变量偏移下的极小极大极限
Conformalized Quantile Regression and Minimax Limits of Fixed-Score Calibration under Known Covariate Shift
做共形预测或不确定性量化的理论党看这篇：CQR 的误差界和 covariate shift 下的极小极大极限都齐了。
论文为 split conformalized quantile regression（CQR）推导了区间长度与条件覆盖的非渐近 L^p 误差界。这些界依赖局部正则性条件与分位数估计的精度保证，并被具体化到稀疏 ReLU 神经网络的分位数回归。针对校准集与测试集协变量分布不同的 covariate shift 场景，论文同样给出非渐近界。在两个构造的 fixed-score 校准基准上，作者证明了已知协变量偏移下期望意义匹配的极小极大上下界：标量问题对所有 p∈[1,∞] 匹配，K-threshold 问题对有限 p 匹配，且后者对任意 p∈[1,∞] 有高概率极小极大下界。
Conformalized Quantile Regression and Minimax Limits of Fixed-Score Calibration under Known Covariate Shift
In this paper, we study nonasymptotic $L^p$ error bounds for interval length and conditional coverage in split conformalized quantile regression (CQR). Our bounds rely on local regularity conditions and accuracy guarantees for the estimated quantiles. We further instantiate our bounds for quantile regression with sparse ReLU neural networks. We also consider covariate shift, where the calibration and test covariates have different distributions, and derive nonasymptotic bounds for this setting. We obtain matching minimax upper and lower bounds in expectation for two constructed fixed-score calibration benchmarks under known covariate shift. The bounds match for every $p\in[1,\infty]$ in the scalar problem and for finite $p$ in the $K$-threshold problem; for the latter, a high-probability minimax lower bound holds for every $p\in[1,\infty]$.