Estimation de la fonction graphon d'un W-graphe. Application au réseau de la blogosphere politique française

Pierre Latouche (1) , Stéphane Robin (2)

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

Networks have been widely used in many scientific fiels, and in particular in social sciences, in order to represent interactions between objects of interest. Since the earlier work of Moreno in 1934, many random graph models have been proposed to extract knowledge from these structured data sets. For instance, the stochastic block model (SBM) allows the search of groups of vertices sharing homogeneous connection profiles. In this work, we consider the W-graph model which is known to generalize many random graph models but for which very few methods exist to perform inference on real data. First, we recall that the SBM model can be represented as a W-graph with a block-constant graphon function. Using a variational Bayes expectation maximization algorithm, we then approximate the posterior distribution over the model parameters of a SBM model and we show how this variational approximation can be integrated in order to estimate the posterior distribution of W-graph graph function. In this Bayesian framework, we also derive the occurrence probability of a motif. In practice, this allows to test if a motif is over-represented in a given network. All the results presented here are tested on simulated data and the French political blogosphere network.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Pierre Latouche, Stéphane Robin. Estimation de la fonction graphon d'un W-graphe. Application au réseau de la blogosphere politique française. 45èmes journées de Statistique, 2013, Toulouse, France. pp.JdS. ⟨hal-00830095⟩