We develop a framework for conformal prediction in dyadic regression problems under complex missingness mechanisms. At the theoretical level, we establish super-uniformity of conformal prediction under distributional invariance conditions weaker than exchangeability. A key result handles the case where the sample itself is a random subset of the index set, a setting not covered by existing theory, via a novel bijection argument that constructs an explicit measure-preserving correspondence between events. In addition, we propose conformal prediction procedures for jointly exchangeable arrays, including full conformal, split conformal, a row-column approach exploiting similarities within rows and columns, and a selective conformal procedure achieving mask-conditional validity. For missing elements, we establish asymptotic validity of a graphon-weighted conformal procedure under a nonparametric graphon model for the missingness mechanism. We further establish conditional validity results for both continuous and discrete responses; to the best of our knowledge, this is first formal proof of asymptotic conditional validity for weighted conformal prediction under a missing-not-at-random assumption. The proposed methods are illustrated on synthetic and real network data.

翻译：我们针对复杂缺失机制下的配对回归问题，提出了一种共形预测框架。在理论层面，我们证明了在弱于可交换性的分布不变性条件下，共形预测具有超均匀性。针对样本本身为索引集随机子集这一现有理论未覆盖的情形，我们通过一种新颖的双射论证构造了事件间显式的保测对应关系，从而给出了关键性结果。此外，我们提出了适用于联合可交换阵列的共形预测方法，包括全共形法、分裂共形法、利用行列相似性的行列法，以及实现掩膜条件有效性的选择性共形法。针对缺失元素，我们在非参数图模型描述的缺失机制下，证明了图加权共形方法的渐近有效性。我们进一步建立了连续型和离散型响应的条件有效性结果——据我们所知，这是首个在非随机缺失假设下加权共形预测渐近条件有效性的严格证明。所提方法在合成数据集与真实网络数据上得到了验证。