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，我们如何量化围绕该预测的不确定性？无分布预测推断旨在构建预测区间，其有效覆盖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（包括一致性预测和jackknife+方法）提供的理论保证是边缘性的（即在对训练数据和测试数据抽取的平均意义上）。相比之下，训练条件覆盖是更强效的有效性概念，能确保测试点在大部分训练数据抽取下具有预测覆盖，因此在实践中更具可取性。Vovk [2012]证明分裂一致性方法具有训练条件覆盖，但Bian与Barber [2023]的最新工作表明，若不做进一步假设，完全一致性方法和jackknife+方法无法实现此类有效性保证。本文证明，在算法稳定性假设下，完全一致性方法和jackknife+方法可满足训练条件覆盖性质。