In a supervised learning problem, given a predicted value that is the output of some trained model, how can we quantify our uncertainty around this prediction? Distribution-free predictive inference aims to construct prediction intervals around this output, with valid coverage that does not rely on assumptions on the distribution of the data or the nature of the model training algorithm. Existing methods in this area, including conformal prediction and jackknife+, offer theoretical guarantees that hold marginally (i.e., on average over a draw of training and test data). In contrast, training-conditional coverage is a stronger notion of validity that ensures predictive coverage of the test point for most draws of the training data, and is thus a more desirable property in practice. Training-conditional coverage was shown by Vovk [2012] to hold for the split conformal method, but recent work by Bian and Barber [2023] proves that such validity guarantees are not possible for the full conformal and jackknife+ methods without further assumptions. In this paper, we show that an assumption of algorithmic stability ensures that the training-conditional coverage property holds for the full conformal and jackknife+ methods.

翻译：在监督学习问题中，给定某个训练模型输出的预测值，我们应如何量化该预测的不确定性？分布无关预测推断旨在围绕该输出构建预测区间，其有效覆盖性不依赖于数据分布或模型训练算法性质的假设。该领域的现有方法（包括共形预测和jackknife+）提供的理论保证是边际成立的（即对训练与测试数据联合分布的平均意义而言）。相比之下，训练条件覆盖是一种更强的有效性概念，它确保在大多数训练数据抽取情形下对测试点的预测覆盖性，因而是实践中更理想的性质。Vovk [2012] 证明分裂共形方法满足训练条件覆盖，但Bian与Barber [2023] 的最新研究证明，若无额外假设，完全共形与jackknife+方法不可能实现此类有效性保证。本文证明：算法稳定性假设可确保完全共形与jackknife+方法满足训练条件覆盖性质。