Mixture models and networks: The stochastic blockmodel. (February 2022)

• Record Type: Journal Article
• Authors: De Nicola, Giacomo; Sischka, Benjamin; Kauermann, Göran
• Other Names: Francis Brian guest-editor.; Hinde John guest-editor.
• Is Part Of: Statistical modelling. Volume 22:Number 1/2(2022)
• Page Start: 67
• Page End: 94
• Publication Date: 2022-02
• Subjects: community detection -- Mixture models -- statistical network analysis -- stochastic blockmodels; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X211033169
• Languages: English
• ISSNs: 1471-082X

Abstract

Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity behaviour, with nodes behaving similarly belonging to the same community. In this context, mixture modelling is pursued through stochastic blockmodelling. We consider stochastic blockmodels and some of their variants and extensions from a mixture modelling perspective. We also explore some of the main classes of estimation methods available and propose an alternative approach based on the reformulation of the blockmodel as a graphon. In addition to the discussion of inferential properties and estimating procedures, we focus on the application of the models to several real-world network datasets, showcasing the advantages and pitfalls of different approaches.