Joint Estimation of Edge Probabilities for Multi-layer Networks via Neighborhood Smoothing

2026-01-28

AI Summary

This study addresses the problem of jointly estimating edge probabilities in multilayer networks by proposing a two-step neighborhood smoothing algorithm. The approach is grounded in a novel three-layer graphical model that incorporates latent layer-position parameters, enabling a unified characterization of structural similarities among nodes and across network layers without requiring strong modeling assumptions. By leveraging nonparametric estimation and a low-complexity design, the method achieves efficient and minimally parameterized inference of joint edge probabilities. Experimental evaluations on both synthetic data and a real-world food import–export network demonstrate that the proposed algorithm significantly outperforms current state-of-the-art methods in link prediction tasks.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In this paper we focus on jointly estimating the edge probabilities for multi-layer networks. We define a novel multi-layer graphon, a ternary function in contrast to the bivariate graphon function in the literature by introducing an additional latent layer position parameter, which is model-free and covers a wide range of multi-layer networks. We develop a computationally efficient two-step neighborhood smoothing algorithm to estimate the edge probabilities of multi-layer networks, which requires little tuning and fully utilize the similarity across both network layers and nodes. Numerical experiments demonstrate the advantages of our method over the existing state-of-the-art ones. A real Worldwide Food Import/Export Network dataset example is analyzed to illustrate the better performance of the proposed method over benchmark methods in terms of link prediction.

Problem

• multi-layer networks
• edge probabilities
• graphon
• link prediction
• network estimation

Innovation

• multi-layer graphon
• neighborhood smoothing
• edge probability estimation
• link prediction
• latent layer position