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