Conformal Prediction for Dyadic Regression Under Complex Missingness

2026-06-09

AI Summary

This work addresses the problem of constructing prediction intervals in binary regression under complex missingness mechanisms. It proposes a conformal prediction framework grounded in a distributional invariance assumption weaker than exchangeability. For the first time, it handles settings where observed samples form a randomly indexed subset, and establishes—via a novel bijective argument—the asymptotic conditional validity of weighted conformal prediction under non-ignorable missingness. The approach integrates techniques from jointly exchangeable array modeling, graph-structured weighting, exploitation of row–column dependencies, and selective conformal inference. Empirical evaluations on both synthetic and real-world network data demonstrate that the method achieves conditional validity guarantees for both continuous and discrete response variables.

Abstract

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.

Problem

• conformal prediction
• dyadic regression
• complex missingness
• missing-not-at-random
• conditional validity

Innovation

• Conformal Prediction
• Dyadic Regression
• Missingness Mechanism
• Graphon Model
• Conditional Validity