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.
Highlights
The underlying idea of a mixture model is rather simple
Though the focus of their paper lies in the modelling of outliers, the authors make use of the idea that a finite mixture model can be comprehended as a missing data problem
The aim of this article is to illuminate on the connection between mixture models and stochastic blockmodels, exploring some of the different approaches within the model class and demonstrating their applicability by making use of real data
Summary
The underlying idea of a mixture model is rather simple. Instead of assuming that the target variable follows a plain distribution, one considers a mixture of multiple distributions. Though the focus of their paper lies in the modelling of outliers, the authors make use of the idea that a finite mixture model can be comprehended as a missing data problem. Under this modelling framework, one assumes that the discrete valued random variable Z takes values {1, ..., K} with
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