Séance Séminaire

Séminaire de Probabilités et Statistique

Variational inference for the stochastic blockmodel

The statistical inference of several models for random graphs has received a great attention in the last decade. Among these models, the stochastic blockmodel (and variations about it) is one of the most popular as it provides a simple description of the heterogeneous structure observed in many networks. This model can be viewed as a mixture model where each node belongs to a class and edges are drawn between the nodes conditionally to they class they belong to.
As for most incomplete data model, the statistical inference is not straightforward and most methods require to retrieve the conditional distribution of the unobserved data (the classes) given the observed ones (the edges). Variational inference provides a general framework to provide an optimal approximation of this distribution, in the sense of the Küllback-Leibler divergence. Based on simulation studies and theoretical results, we will show that, due to an asymptotic framework that is specific to networks, the variational approximation is efficient.
We will illustrate these works with applications in molecular biology and ecology. We will eventually introduce ongoing works on other models for heterogeneous graph.