Conformal Predictive Systems (CPS) offer a versatile framework for
constructing predictive distributions, allowing for calibrated inference and
informative decision-making. However, their applicability has been limited to
scenarios adhering to the Independent and Identically Distributed (IID) model
assumption. This paper extends CPS to accommodate scenarios characterized by
covariate shifts. We therefore propose Weighted CPS (WCPS), akin to Weighted
Conformal Prediction (WCP), leveraging likelihood ratios between training and
testing covariate distributions. This extension enables the construction of
nonparametric predictive distributions capable of handling covariate shifts. We
present theoretical underpinnings and conjectures regarding the validity and
efficacy of WCPS and demonstrate its utility through empirical evaluations on
both synthetic and real-world datasets. Our simulation experiments indicate
that WCPS are probabilistically calibrated under covariate shift.

该论文提出了一种适应协变量偏移的加权一致性预测系统（WCPS），通过利用训练和测试协变量分布之间的似然比，构建非参数预测分布，并通过模拟实验证明了其在协变量偏移下的概率校准性。