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：保形预测方法能够在有限样本下提供边缘覆盖的预测集，但许多实际应用需要能适应个体测试点、子群体或数据结构成分的覆盖保证。现有针对条件覆盖的方法大多采用个案分析方式，缺乏理解条件误覆盖来源、比较不同流程优劣以及将此类保证扩展到独立同分布数据之外的一般性理论。我们通过提出针对条件覆盖的保形方法统一框架与理论来填补这些空白。核心贡献在于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内在条件失配误差。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，具体应用于图结构和层次结构场景。数值实验验证了理论结果并展示了所提方法的有效性。