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

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2013
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https://hal.archives-ouvertes.fr/hal-00876334
Contributeur : Pierre Latouche <>
Soumis le : jeudi 24 octobre 2013 - 12:07:16
Dernière modification le : mercredi 4 janvier 2017 - 16:18:51

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  • HAL Id : hal-00876334, version 1
  • ARXIV : 1310.6150

Citation

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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