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。

协变量漂移下的一致性预测系统

Conformal Predictive Systems Under Covariate Shift

Conformal predictive systems are a recent modification of conformal
predictors that output, in regression problems, probability distributions for
labels of test observations rather than set predictions. The extra information
provided by conformal predictive systems may be useful, e.g., in decision
making problems. Conformal predictive systems inherit the relative
computational inefficiency of conformal predictors. In this paper we discuss
two computationally efficient versions of conformal predictive systems, which
we call split conformal predictive systems and cross-conformal predictive
systems. The main advantage of split conformal predictive systems is their
guaranteed validity, whereas for cross-conformal predictive systems validity
only holds empirically and in the absence of excessive randomization. The main
advantage of cross-conformal predictive systems is their greater predictive
efficiency.

本文介绍了两个计算效率更高的一类回归问题的概率分布预测方法，分别为 “分裂式 conformal 预测系统” 和 “交叉式 conformal 预测系统”；前者更保证准确性，后者更具预测效率，但其有效性仅在排除过度随机化的情况下成立。