Inference in Stochastic Block Models from Missing Data

This work deals with nonobserved dyads during the sampling of a network and consecutive issues in the inference of the stochastic block model (SBM). We review sampling designs and recover missing at random (MAR) and not missing at random (NMAR) conditions for the SBM. We introduce variants of the variational EM algorithm for inferring the SBM, possibly in the presence of external covariates, under various sampling designs (MAR and NMAR). Identifiability issues are discussed for some sampling designs. Model selection criteria based on integrated classification likelihood are derived for selecting both the number of blocks and the sampling design. We investigate the accuracy and the range of applicability of these algorithms with simulations. We explore several real-world networks with an R/C++ package implementing our approach.

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