找到最优数据划分方式,让预测区间更短且保证覆盖率。
On Optimal Data Splitting for Split Conformal Prediction
- 提出理论框架,分析训练与校准数据的最优分配比例。
- 在线性、非参数及神经网络回归中验证了方法有效性。
- 提供可操作的数据驱动选择策略,适合需要精准预测的场景。
分拆式合约定理及其变体提供了一种无需分布假设的不确定性量化框架,通过构建具有有限样本覆盖率保证的预测区间或集合来实现。这些区间的统计效率高度依赖于数据划分为训练集和校准集的方式。尽管这一问题在实践中至关重要,但如何在保证覆盖率的前提下最小化预测区间长度,其理论指导仍不明确。本文建立了分拆式合约定理中的最优数据划分理论框架。首先在一般设定下分析该问题,推导出对称与非对称情形下的长度最优划分比例解析表达式;随后将通用结果应用于线性回归、非参数回归及神经网络等常见回归场景,展现框架的广泛适用性。我们还提出一种基于数据的方法来选择最优比例。分析揭示了模型特性如何决定样本在训练与校准之间的最优分配,为构造更短预测区间提供了原则性指导。在合成与真实数据集上的实验验证了该方法在多种实际场景中的适用性。
原文摘要 · Abstract (English)
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.
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