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This research establishes precise information-theoretic thresholds for recovering node alignments in Gaussian graph matching when both structural edge weights and contextual node features are present. By demonstrating that the inclusion of node-level context decouples exact recovery from partial recovery, the study provides a critical benchmark for designing efficient algorithms in high-dimensional settings where prior all-or-nothing phase transitions no longer apply.
Sharp Statistical Thresholds for Attributed Gaussian Graph Matching
arXiv:2603.23305v2 Announce Type: replace-cross Abstract: We investigate the problem of matching networks where both edge weights and node features are correlated following a specific node correspondence. While prior work has established sharp thresholds for matching either graphs or features individually, the joint setting has been significantly less explored. In this study, we derive precise information-theoretic thresholds for exact recovery, almost-exact recovery, and partial recovery of the underlying alignment. These are expressed in terms of graph and feature correlation strengths, the number of nodes, and the dimension of the features. Interestingly, whereas an all-or-nothing phase transition is observed in the standard graph-matching scenario, the inclusion of contextual information at the node level introduces a richer structure: the exact-recovery threshold separates from the shared threshold for almost-exact and partial recovery. Closing gaps left by prior works, we provide a sharp characterization of the thresholds governing how structural and contextual information interact in graph matching, and thereby establish a benchmark for designing efficient algorithms in the high-dimensional setting.
Abstract:We investigate the problem of matching networks where both edge weights and node features are correlated following a specific node correspondence. While prior work has established sharp thresholds for matching either graphs or features individually, the joint setting has been significantly less explored. In this study, we derive precise information-theoretic thresholds for exact recovery, almost-exact recovery, and partial recovery of the underlying alignment. These are expressed in terms of graph and feature correlation strengths, the number of nodes, and the dimension of the features. Interestingly, whereas an all-or-nothing phase transition is observed in the standard graph-matching scenario, the inclusion of contextual information at the node level introduces a richer structure: the exact-recovery threshold separates from the shared threshold for almost-exact and partial recovery. Closing gaps left by prior works, we provide a sharp characterization of the thresholds governing how structural and contextual information interact in graph matching, and thereby establish a benchmark for designing efficient algorithms in the high-dimensional setting.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2603.23305 [stat.ML]
(or arXiv:2603.23305v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2603.23305 Focus to learn more arXiv-issued DOI via DataCite
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