Early stopping based on hold-out data is a popular regularization technique designed to mitigate overfitting and increase the predictive accuracy of neural networks. Models trained with early stopping often provide relatively accurate predictions, but they generally still lack precise statistical guarantees unless they are further calibrated using independent hold-out data. This paper addresses the above limitation with conformalized early stopping: a novel method that combines early stopping with conformal calibration while efficiently recycling the same hold-out data. This leads to models that are both accurate and able to provide exact predictive inferences without multiple data splits nor overly conservative adjustments. Practical implementations are developed for different learning tasks -- outlier detection, multi-class classification, regression -- and their competitive performance is demonstrated on real data.

翻译：基于留出数据的早停法是一种流行的正则化技术，旨在减轻过拟合并提高神经网络的预测准确性。采用早停法训练的模型通常能提供相对准确的预测，但通常仍缺乏精确的统计保证，除非使用独立的留出数据进行进一步校准。本文通过共形化早停法解决了上述局限：这是一种新型方法，将早停法与共形校准相结合，同时高效地复用相同的留出数据。这使模型既能实现准确性，又能提供精确的预测推断，无需多种数据分割或保守的调整。针对不同学习任务——异常检测、多类分类、回归——开发了实用实现，并在真实数据上展示了其具有竞争力的性能。