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）是一种最近提出的技术，它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）的推广，CRC确保从点预测器提取的集合预测器能够控制风险函数，例如误覆盖概率或假阴性率。原始CRC要求将可用数据集划分为训练集和验证集。当数据可用性有限时，这会导致集合预测器效率低下。本文提出了一种基于交叉验证而非原始CRC中验证的新方法。所提出的交叉验证CRC（CV-CRC）将CP中的jackknife-minmax版本扩展到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保证。此外，数值实验显示，在可用数据有限的情况下，CV-CRC相较于CRC能降低平均集合大小。