Bayesian Model Averaging of Stochastic Block Models to Estimate the Graphon Function and Motif Frequencies in a W-graph Model - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2013

Bayesian Model Averaging of Stochastic Block Models to Estimate the Graphon Function and Motif Frequencies in a W-graph Model

Résumé

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. The stochastic block model is a special case of W-graph where the graphon function is block-wise constant. In this paper, we propose a variational Bayes approach to estimate the W-graph as an average of stochastic block models with increasing number of blocks. We derive a variational Bayes algorithm and the corresponding variational weights for model averaging. 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.

Dates et versions

hal-00876334 , version 1 (24-10-2013)

Identifiants

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Pierre Latouche, Stéphane Robin. Bayesian Model Averaging of Stochastic Block Models to Estimate the Graphon Function and Motif Frequencies in a W-graph Model. 2013. ⟨hal-00876334⟩
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