Efficient inference in stochastic block models with vertex labels

International audienceWe study the stochastic block model with twocommunities where vertices contain side information in the formof a vertex label. These vertex labels may have arbitrary labeldistributions, depending on the community memberships. Weanalyze a linearized version of the popular belief propagationalgorithm. We show that this algorithm achieves the highestaccuracy possible whenever a certain function of the networkparameters has a unique fixed point. Whenever this function hasmultiple fixed points, the belief propagation algorithm may notperform optimally. We show that increasing the information inthe vertex labels may reduce the number of fixed points andhence lead to optimality of belief propagation