Estimation and Statistical Inference for Generalized Multilayer Latent Space Model

2026-02-22

AI Summary

This study addresses the lack of an effective statistical inference framework for multilayer directed networks, particularly when handling heterogeneous edge types and layer-specific structures. The authors propose a generalized multilayer latent space model that assigns each node distinct sender and receiver latent positions and introduces inter-layer connectivity matrices. Observed networks are modeled via a nonlinear link function as a tensor amenable to Tucker low-rank decomposition, and parameter estimation is achieved through a matricization-fusion approach. For the first time, the paper establishes theoretical guarantees—consistency and asymptotic normality—for both latent positions and connectivity matrices under this model, enabling confidence region construction and hypothesis testing for inter-layer structural equivalence. Simulations and real-data analyses demonstrate the method’s statistical efficiency and practical utility.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for multilayer networks remains underdeveloped. In this paper, we propose a flexible latent space model for multilayer directed networks with various edge types, where each node is assigned with two latent positions capturing sending and receiving behaviors, and each layer has a connection matrix governing the layer-specific structure. Through nonlinear link functions, the proposed model represents the structure of a multilayer network as a tensor, which admits a Tucker low-rank decomposition. This formulation poses significant challenges on the estimation and statistical inference for the latent positions and connection matrices, where existing techniques are inapplicable. To tackle this issue, a novel unfolding and fusion method is developed to facilitate estimation. We establish both consistency and asymptotic normality for the estimated latent positions and connection matrices, which paves the way for statistical inference tasks in multilayer network applications, such as constructing confidence regions for the latent positions and testing whether two network layers share the same structure. We validate the proposed method through extensive simulation studies and demonstrate its practical utility on real-world data.

Problem

• multilayer networks
• latent space model
• statistical inference
• tensor decomposition
• network estimation

Innovation

• multilayer network
• latent space model
• Tucker decomposition
• statistical inference
• asymptotic normality