# Variational Estimators for Node Popularity Models

arXiv: https://arxiv.org/abs/2511.17783 · HTML: https://mlsanity.com/paper/2511.17783/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 21 Nov 2025.

## Builds on (most cited first, 11 of 11)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Statistical clustering of temporal networks through a dynamic stochastic block model](https://mlsanity.com/paper/1506.07464/) (2015)
- [Coauthorship and Citation Networks for Statisticians](https://mlsanity.com/paper/1410.2840/) (2014)
- [Analysis of spectral clustering algorithms for community detection: the general bipartite setting](https://mlsanity.com/paper/1803.04547/) (2018)
- [Spectral Algorithms for Community Detection in Directed Networks](https://mlsanity.com/paper/2008.03820/) (2020)
- [Fast Network Community Detection with Profile-Pseudo Likelihood Methods](https://mlsanity.com/paper/2011.00647/) (2020)
- [A Survey on Theoretical Advances of Community Detection in Networks](https://mlsanity.com/paper/1809.07691/) (2018)
- [Dynamic stochastic blockmodels: Statistical models for time-evolving networks](https://mlsanity.com/paper/1304.5974/) (2013)
- [Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks](https://mlsanity.com/paper/2206.08465/) (2022)
- [Two-way Node Popularity Model for Directed and Bipartite Networks](https://mlsanity.com/paper/2412.08051/) (2024)

## Abstract (arXiv)

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.