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Variational Bayes model averaging for graphon functions and motif frequencies inference in \(W\)-graph models. (English) Zbl 1349.62081

Summary: \(W\)-graph refers to a general class of random graph models that can be seen as a random graph limit. It is characterized by both its graphon function and its motif frequencies. In this paper, relying on an existing variational Bayes algorithm for the stochastic block models (SBMs) along with the corresponding weights for model averaging, we derive an estimate of the graphon function as an average of SBMs with increasing number of blocks. In the same framework, we derive the variational posterior frequency of any motif. A simulation study and an illustration on a social network complete our work.

MSC:

62F15 Bayesian inference
05C80 Random graphs (graph-theoretic aspects)
62G05 Nonparametric estimation
91D30 Social networks; opinion dynamics
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