Optimality of variational inference for stochastic block model with missing links

TL;DR

This paper proves that variational inference provides a minimax optimal and computationally feasible estimator for stochastic block models with missing links, supported by theoretical guarantees and empirical validation.

Contribution

It establishes the first minimax optimal variational estimator for stochastic block models with missing links, extending the theoretical understanding of these methods.

Findings

Variational approximation converges at the minimax rate.

The estimator outperforms existing methods in simulations.

Numerical studies confirm practical advantages.

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.