Variational Bayes model averaging for graphon functions and motif frequencies inference in W-graph models

Pierre Latouche (1) , Stephane S. Robin (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 MIA-Paris - Mathématiques et Informatique Appliquées

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 along with the corresponding weights for model averaging, we derive an estimate of the graphon function as an average of stochastic block models 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.

Mots clés: stochastic block model; W -graph; Bayesian model averaging; graphon; network; network motif

Domaines: Statistiques [math.ST]

Pierre Latouche, Stephane S. Robin. Variational Bayes model averaging for graphon functions and motif frequencies inference in W-graph models. Statistics and Computing, 2016, 26 (6), pp.1173 - 1185. ⟨10.1007/s11222-015-9607-0⟩. ⟨hal-01519750⟩