Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing methods targeting conditional coverage are largely analyzed case by case, leaving limited general theory for understanding where conditional miscoverage comes from, how different procedures should be compared, and how such guarantees can be extended beyond i.i.d.~data. We address these gaps through a unified framework and theory for conformal methods targeting conditional coverage. Our central contribution is a non-asymptotic decomposition of conditional miscoverage into three interpretable components: score-estimation error, finite-sample calibration error, and intrinsic conditional-mismatch error. This decomposition clarifies the mechanisms behind asymptotic conditional validity and places existing methods within a common analytical lens. Building on this framework, we derive principled guidance for conditional-coverage-oriented model selection, and develop localized methods with asymptotic conditional guarantees under covariate shift. Finally, we extend the framework to structured data, with concrete applications to graph-structured and hierarchical settings. Numerical experiments corroborate the theory and demonstrate the effectiveness of the proposed procedures.

翻译：摘要：共形预测提供具有有限样本边际覆盖的预测集，但许多应用需要能适应个体测试点、子群体或数据结构性组分的覆盖保证。现有针对条件覆盖的方法大多采用逐案例分析，缺乏理解条件误覆盖来源、不同过程比较方式以及如何将此类保证扩展到独立同分布数据之外的通用理论。我们通过针对条件覆盖的共形方法的统一框架与理论填补这些空白。核心贡献是将条件误覆盖非渐近分解为三个可解释分量：分数估计误差、有限样本校准误差和固有条件不匹配误差。该分解阐明了渐近条件有效性背后的机制，并将现有方法置于统一分析视角下。基于此框架，我们推导出面向条件覆盖的模型选择原则性指导，并开发了在协变量偏移下具有渐近条件保证的局部化方法。最后，我们将该框架扩展到结构化数据，具体应用于图结构与层级结构场景。数值实验验证了理论分析并展示了所提流程的有效性。