Doubly-Unlinked Regression for Dependent Data

2026-03-19

AI Summary

This study addresses the dual mismatch regression problem, where both covariate–response pairs and response–latent spatiotemporal domain correspondences are scrambled by unknown permutations and further entangled by unobserved stochastic processes inducing dependence. To tackle this challenge, the authors propose REPAIR, a variational Bayesian algorithm grounded in a block-structured permutation model that effectively captures local shuffling while substantially reducing computational complexity. Theoretical analysis demonstrates that consistent estimation of regression coefficients is achievable under conditions weaker than exact permutation recovery, and delineates the role of signal-to-noise ratio in influencing both parameter estimation and permutation recovery accuracy. Extensive simulations and empirical analyses corroborate the method’s efficacy and support the theoretical findings. This work constitutes the first systematic treatment of such dual mismatch settings, unifying frameworks for shuffled regression and implicit domain permutation modeling.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Shuffled regression concerns settings in which covariates and responses are observed without their correct pairing. In dependent-data problems, a second form of missing correspondence can arise when responses are also detached from the latent temporal, spatial, or geometric domain that induces their dependence structure. We study regression under this joint loss of correspondence and, to our knowledge, provide the first systematic treatment of this setting. Specifically, we consider a doubly-unlinked regression model in which both the covariate-response link and the response-domain link are unknown, represented by two latent permutation matrices, while dependence is induced by an unobserved stochastic process. This framework unifies shuffled regression and latent-domain permutation models within a common dependent-data setting. We characterize signal-to-noise regimes governing recovery of the regression parameter and the latent permutations, and show that consistent estimation of the regression coefficient can be achieved under strictly weaker conditions than exact permutation recovery. To address the combinatorial difficulty of inference, we develop REPAIR, a variational Bayes method based on a block-structured permutation model that captures localized scrambling while substantially reducing computational complexity. Simulations and an applied example illustrate the empirical behavior of REPAIR and support the theoretical results.

Problem

• shuffled regression
• dependent data
• latent permutation
• unlinked correspondence
• regression under missing correspondence

Innovation

• doubly-unlinked regression
• permutation recovery
• dependent data
• variational Bayes
• shuffled regression