Statistical Modelling 22 (1&2) (2022), 67–94
Mixture models and networks: The stochastic blockmodel
Giacomo De Nicola,
Department of Statistics,
Faculty of Mathematics,
Informatics and Statistics,
Ludwig-Maximilians-Universität München,
Munich,
Germany.
Benjamin Sischka,
Department of Statistics,
Faculty of Mathematics,
Informatics and Statistics,
Ludwig-Maximilians-Universität München,
Munich,
Germany.
Göran Kauermann,
Department of Statistics,
Faculty of Mathematics,
Informatics and Statistics,
Ludwig-Maximilians-Universität München,
Munich,
Germany.
e-mail: goeran.kauermann@stat.uni-muenchen.de
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.
Keywords:
community detection, Mixture models, statistical network analysis, stochastic blockmodels
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