Conformal Prediction for Dyadic Regression Under Complex Missingness

• URL: http://arxiv.org/abs/2606.11136v2
• Date: Tue, 16 Jun 2026 21:21:28 GMT
• Title: Conformal Prediction for Dyadic Regression Under Complex Missingness
• Abstract summary: We develop a framework for conformal prediction in dyadic regression problems under complex missingness mechanisms.<n>We establish conditional validity results for both continuous and discrete responses.<n>This is the first formal proof of conditional validity for weighted conformal prediction under a missing-not-at-random assumption.
• Score: 2.7512870037345696
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a framework for conformal prediction in dyadic regression problems under complex missingness mechanisms. At the theoretical level, we develop general technical tools for establishing finite-sample validity 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 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 the 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.

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