Optimality of variational inference for stochasticblock model with missing links

Solenne Gaucher, Olga Klopp

Keywords: Network models, link prediction, variational methods, maximum likelihood

TL;DR: We show that the tractable variational approximation to the maximum likelihood estimator is minimax optimal in the stochastic block model, and show its advantages over current methods on simulated and real networks.

Abstract: 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.

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