Conformal risk control (CRC) is a recently proposed technique that applies post-hoc to a conventional point predictor to provide calibration guarantees. Generalizing conformal prediction (CP), with CRC, calibration is ensured for a set predictor that is extracted from the point predictor to control a risk function such as the probability of miscoverage or the false negative rate. The original CRC requires the available data set to be split between training and validation data sets. This can be problematic when data availability is limited, resulting in inefficient set predictors. In this paper, a novel CRC method is introduced that is based on cross-validation, rather than on validation as the original CRC. The proposed cross-validation CRC (CV-CRC) extends a version of the jackknife-minmax from CP to CRC, allowing for the control of a broader range of risk functions. CV-CRC is proved to offer theoretical guarantees on the average risk of the set predictor. Furthermore, numerical experiments show that CV-CRC can reduce the average set size with respect to CRC when the available data are limited.

翻译：共形风险控制（CRC）是一种近期提出的技术，可后验地应用于传统点预测器以提供校准保证。作为共形预测（CP）的泛化方法，CRC确保从点预测器中提取的集合预测器在控制风险函数（如误覆盖率或假阴性率）时得到校准。原始CRC要求将可用数据集划分为训练集和验证集，这在数据量有限时可能导致集合预测器效率低下。本文提出一种基于交叉验证而非原始CRC中验证的新型CRC方法。所提出的交叉验证CRC（CV-CRC）将CP中的jackknife-minmax方法扩展至CRC，从而能够控制更广泛的风险函数。理论证明表明CV-CRC能为集合预测器的平均风险提供理论保证。此外，数值实验显示，在可用数据有限时，CV-CRC相较于CRC能降低平均集合规模。