用最优传输方法解决测试数据分布偏移下的置信预测问题
Non-exchangeable Conformal Prediction with Optimal Transport: Tackling Distribution Shifts with Unlabeled Data
- 基于最优传输理论重构校准数据分布，捕捉分布偏移
- 无需先验分布偏移信息即可估计并补偿置信度损失
- 适用于任意未知分布偏移场景，适合高可靠性需求应用
置信预测是一种无需假设数据分布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。其主流方法——分片置信预测，计算高效，仅需在未见校准数据上收集模型预测统计量。然而，该方法的保证前提是校准数据与测试数据可交换，这一条件难以验证且常因分布偏移而被破坏。现有缓解方法虽能提升覆盖率，但通常依赖对测试时可能发生的分布偏移类型的先验知识。本文提出新视角：通过最优传输理论研究该问题，证明可估计覆盖率损失并有效应对任意分布偏移，提供一种原理严谨、普适性强的解决方案。
原文摘要 · Abstract (English)
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.
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