Title: T-GINEE: A Tensor-Based Multi-Graph Representation Learning
Primary area: learning on graphs and other geometries & topologies
Keywords: multilayer networks, tensor decomposition, generalized estimating equations, network analysis, cross-layer dependencies, partial alignment, statistical regularization

Abstract: While traditional network analysis focuses on single-layer networks, real-world systems often exhibit multiple types of relationships simultaneously, forming multilayer networks. However, existing multilayer network analysis methods typically assume complete node correspondences across layers, which is unrealistic in practice. Furthermore, these methods either treat different layers independently or simply aggregate them, failing to capture complex interdependencies between layers. To address these challenges, we propose T-GINEE (Tensor-based Generalized Multilayer-graph Estimating Equation), a statistical regularization framework that combines tensor-based generalized estimating equations with task-specific loss to explicitly model cross-network correlations. The key technical innovations include: (1) A CP tensor decomposition approach that captures structural dependencies through shared latent factors; (2) A generalized estimating equation framework that models inter-layer correlations through working covariance matrices; (3) A flexible link function design that accommodates various network characteristics, including sparsity. Our theoretical analysis establishes consistency and asymptotic normality of T-GINEE under mild regularity conditions. Extensive experiments on both synthetic and real-world datasets validate the effectiveness of T-GINEE and its practicality for analyzing partially aligned multilayer networks. The code is available in the supplementary material for reproducibility.