Variational Estimators for Node Popularity Models

TL;DR

This paper introduces a variational EM framework for the Two-Way Node Popularity Model, improving estimation accuracy and theoretical guarantees in bipartite network analysis.

Contribution

It develops a computationally efficient variational estimator with proven label consistency for bipartite networks, advancing community detection methods.

Findings

Achieves superior estimation accuracy in simulations

Demonstrates robustness on real-world networks

Provides theoretical guarantees for community label consistency

Abstract

Node popularity is recognized as a key factor in modeling real-world networks, capturing heterogeneity in connectivity across communities. This concept is equally important in bipartite networks, where nodes in different partitions may exhibit varying popularity patterns, motivating models such as the Two-Way Node Popularity Model (TNPM). Existing methods, such as the Two-Stage Divided Cosine (TSDC) algorithm, provide a scalable estimation approach but may have limitations in terms of accuracy or applicability across different types of networks. In this paper, we develop a computationally efficient and theoretically justified variational expectation-maximization (VEM) framework for the TNPM. We establish label consistency for the estimated community assignments produced by the proposed variational estimator in bipartite networks. Through extensive simulation studies, we show that our method achieves superior estimation accuracy across a range of bipartite as well as undirected networks compared to existing algorithms. Finally, we evaluate our method on real-world bipartite and undirected networks, further demonstrating its practical effectiveness and robustness.