Optimal Sampling and Clustering in the Stochastic Block Model

This paper investigates the design of joint adaptive sampling and clustering algorithms in networks whose structure follows the celebrated Stochastic Block Model (SBM). To extract hidden clusters, the interaction between edges (pairs of nodes) may be sampled sequentially, in an adaptive manner. We derive information-theoretical upper bounds on the cluster recovery rate. These bounds actually reveal the optimal sequential edge sampling strategy, and interestingly, the latter does not depend on the sampling budget, but on the parameters of the SBM only. We devise a joint sampling and clustering algorithm matching the recovery rate upper bounds.