Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal prediction, is also computationally efficient as it boils down to collecting statistics of the model predictions on some calibration data not yet seen by the model. Nonetheless, these guarantees only hold if the calibration and test data are exchangeable, a condition that is difficult to verify and often violated in practice due to so-called distribution shifts. The literature is rife with methods to mitigate the loss in coverage in this non-exchangeable setting, but these methods require some prior information on the type of distribution shift to be expected at test time. In this work, we study this problem via a new perspective, through the lens of optimal transport, and show that it is possible to estimate the loss in coverage and mitigate arbitrary distribution shifts, offering a principled and broadly applicable solution.

翻译：置信预测是一种无需分布假设的不确定性量化方法，因其有限样本保证和易用性在机器学习领域广受欢迎。其最常见的变体——分割置信预测——同样计算高效，因为它本质上只需收集模型在部分未见过校准数据上的预测统计量。然而，这些保证仅在校准数据与测试数据可交换的条件下成立，这一条件在实践中难以验证且常因所谓的分布偏移而被违反。现有文献提出了多种缓解非可交换场景下覆盖率损失的方法，但这些方法均需预先掌握测试阶段预期分布偏移类型的信息。本研究通过最优传输这一新视角探讨该问题，证明能够估计覆盖率损失并缓解任意分布偏移，从而提供一种原理清晰且广泛适用的解决方案。