发表机构
HSE University; Lomonosov Moscow State University; Laboratoire de Recherche d’EPITA; University of Duisburg-Essen; Mohamed bin Zayed University of Artificial Intelligence (MBZUAI)（高等经济大学; 罗蒙诺索夫莫斯科国立大学; EPITA研究实验室; 杜伊斯堡-埃森大学; 穆罕默德·本·扎耶德人工智能大学（MBZUAI））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为分裂保形分位数回归建立非渐近$L^p$误差界，并在已知协变量偏移下推导匹配的极小极大上下界，适用于稀疏ReLU网络。\n
AI 中文摘要
本文研究了分裂保形分位数回归（CQR）中间隔长度和条件覆盖率的非渐近$L^p$误差界。我们的界依赖于局部正则性条件以及估计分位数的准确性保证。我们进一步将我们的界应用于具有稀疏ReLU神经网络的回归分位数。我们还考虑了协变量偏移，即校准和测试协变量具有不同的分布，并推导了该设置的非渐近界。在已知协变量偏移下，我们为两个构造的固定评分校准基准获得了期望中匹配的极小极大上界和下界。在标量问题中，这些界对于每个$p\in[1,\infty]$都匹配；在$K$-阈值问题中，对于有限$p$匹配；对于后者，对每个$p\in[1,\infty]$都成立高概率极小极大下界。
英文摘要
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 $p\in[1,\infty]$.
Comments65 pages, 3 figures
