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.

翻译：共形预测系统（CPS）为构建预测分布提供了一种通用框架，可实现校准推断与信息性决策。然而，其适用性此前局限于满足独立同分布（IID）模型假设的场景。本文扩展了CPS以适用于协变量转移的场景。因此，我们提出加权共形预测系统（WCPS），类似于加权共形预测（WCP），利用训练与测试协变量分布之间的似然比。这一扩展使得构建能够处理协变量转移的非参数预测分布成为可能。我们提出了关于WCPS有效性与效力的理论基础与猜想，并通过合成数据集与实际数据集的实证评估展示了其实用性。仿真实验表明，WCPS在协变量转移下具有概率校准性。