这篇论文教你怎么分割数据能让预测区间更短，覆盖了线性回归、神经网络等常见模型，有实操方法。
本文研究分割共形预测中训练集与校准集的最优分割比例，目标是在保持覆盖保证的同时最小化预测区间长度。在一般框架下推导了对称和非对称场景下长度最优分割比的理论刻画，并具体分析了线性回归、非参数回归和神经网络等常见回归设置。提出了一种基于数据的最优比例选择方法，并通过合成和真实数据集实验验证了其适用性。
On Optimal Data Splitting for Split Conformal Prediction
Conformal prediction and its variants, including the split conformal prediction, provide a distribution-free framework for uncertainty quantification by constructing prediction intervals or sets with finite-sample coverage guarantees. The statistical efficiency of these intervals depends critically on how the data are split into training and calibration samples. Despite its practical importance, a principled characterization of the training-calibration split that minimizes prediction interval length while maintaining coverage has remained largely unresolved. In this paper, we develop a theoretical framework for optimal data splitting in split conformal prediction. We first analyze the problem in a general setting and derive analytical characterizations of the length-optimal split ratio under both symmetric and asymmetric regimes. We then show how the general results specialize to several commonly used regression settings, including linear regression, nonparametric regression, and neural networks, thereby demonstrating the scope of the framework. We also describe a data-based method for selecting the optimal proportion. Our analysis clarifies how model-related features govern the optimal allocation of samples between training and calibration and provides principled guidance for constructing shorter prediction intervals. Experiments on both synthetic and real-world datasets demonstrate the applicability of the proposed methodology across a variety of practical scenarios.