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

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. 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.

References in corpus (4)

• Uncovering latent structure in valued graphs: A variational approach
• The method of moments and degree distributions for network models
• Multifractal Network Generator
• Subsampling bootstrap of count features of networks

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• Joint Network Topology Inference via a Shared Graphon Model
• EM-Based Smooth Graphon Estimation Using Bayesian and Spline-Based Approaches
• Nonparametric Two-Sample Test for Networks Using Joint Graphon Estimation