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The stochastic block model (SBM) is a generative model revealing macroscopicstructures in graphs. Bayesian methods are used for (i) cluster assignmentinference and (ii) model selection for the number of clusters. In this paper,we study the behavior of Bayesian inference in the SBM in the large samplelimit. Combining variational approximation and Laplace's method, a consistentcriterion of the fully marginalized log-likelihood is established. Based onthat, we derive a tractable algorithm that solves tasks (i) and (ii)concurrently, obviating the need for an outer loop to check all modelcandidates. Our empirical and theoretical results demonstrate that our methodis scalable in computation, accurate in approximation, and concise in modelselection.

A Tractable Fully Bayesian Method for the Stochastic Block Model