Robust Conformal Prediction under Distribution Shift via
  Physics-Informed Structural Causal Model
Rui Xu Yue Sun Chao Chen Parv Venkitasubramaniam Sihong Xie
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.