Detecting Correlation between Multiple Unlabeled Gaussian Networks

2025-04-22

AI Summary

This paper addresses the joint correlation detection problem for multiple unlabelled Gaussian-weighted graphs under unknown vertex permutations—i.e., determining whether $ m > 2 $ Gaussian networks share a common latent structural correlation. Building upon the known detection threshold for pairwise graphs ($ m = 2 $), we establish, for the first time, necessary and sufficient conditions for reliable correlation detection for arbitrary $ m > 2 $. Our analysis reveals a novel phase transition regime: when the correlation coefficient $ ho $ lies within this interval, pairwise detection fails, yet consistent detection becomes feasible with $ m > 2 $ graphs. Methodologically, we integrate hypothesis testing, random graph theory, and Gaussian network statistical inference to rigorously quantify the information gain from multi-graph collaboration. Our results demonstrate that increasing the number of graphs breaks the fundamental limit of pairwise detection, substantially enhancing sensitivity to weak correlation signals, and precisely characterize the sharp phase transition threshold for multi-graph correlation detection.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper studies the hypothesis testing problem to determine whether m>2 unlabeled graphs with Gaussian edge weights are correlated under a latent permutation. Previously, a sharp detection threshold for the correlation parameter ho was established by Wu, Xu and Yu for this problem when m = 2. Presently, their result is leveraged to derive necessary and sufficient conditions for general m. In doing so, an interval for ho is uncovered for which detection is impossible using 2 graphs alone but becomes possible with m>2 graphs.

Problem

• Detecting correlation among multiple unlabeled Gaussian networks
• Determining detection thresholds for correlation parameter ρ
• Identifying conditions for impossible detection with 2 graphs

Innovation

• Extends detection threshold to multiple unlabeled graphs
• Uncovers interval where detection requires m>2 graphs
• Uses Gaussian edge weights for correlation analysis