Uncertainty is critical to reliable decision-making with machine learning. Conformal prediction (CP) handles uncertainty by predicting a set on a test input, hoping the set to cover the true label with at least $(1-\alpha)$ confidence. This coverage can be guaranteed on test data even if the marginal distributions $P_X$ differ between calibration and test datasets. However, as it is common in practice, when the conditional distribution $P_{Y|X}$ is different on calibration and test data, the coverage is not guaranteed and it is essential to measure and minimize the coverage loss under distributional shift at \textit{all} possible confidence levels. To address these issues, we upper bound the coverage difference at all levels using the cumulative density functions of calibration and test conformal scores and Wasserstein distance. Inspired by the invariance of physics across data distributions, we propose a physics-informed structural causal model (PI-SCM) to reduce the upper bound. We validated that PI-SCM can improve coverage robustness along confidence level and test domain on a traffic speed prediction task and an epidemic spread task with multiple real-world datasets.

翻译：不确定性对于基于机器学习的可靠决策至关重要。共形预测通过为测试输入预测一个集合来处理不确定性，期望该集合以至少$(1-\alpha)$的置信度覆盖真实标签。即使标定数据集与测试数据集的边际分布$P_X$存在差异，这种覆盖保证仍可成立。然而在实际场景中，当标定数据与测试数据的条件分布$P_{Y|X}$不同时，覆盖保证将失效，此时必须在\textit{所有}可能的置信水平下测量并最小化分布偏移导致的覆盖损失。为解决这些问题，我们利用标定集与测试集共形得分的累积分布函数以及Wasserstein距离，对所有置信水平下的覆盖差异进行上界界定。受物理定律跨数据分布不变性的启发，我们提出一种物理信息结构因果模型以降低该上界。通过交通速度预测任务与传染病传播任务上的多个真实数据集验证，PI-SCM能够沿置信水平和测试域维度提升覆盖鲁棒性。