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Variational methods are extremely popular in the analysis of network data.Statistical guarantees obtained for these methods typically provide asymptoticnormality for the problem of estimation of global model parameters under thestochastic block model. In the present work, we consider the case of networkswith missing links that is important in application and show that thevariational approximation to the maximum likelihood estimator converges at theminimax rate. This provides the first minimax optimal and tractable estimatorfor the problem of parameter estimation for the stochastic block model withmissing links. We complement our results with numerical studies of simulatedand real networks, which confirm the advantages of this estimator over currentmethods.

Optimality of variational inference for stochastic block model with missing links