# Optimality of variational inference for stochastic block model with missing links Source: [Optimality of variational inference for stochastic block model with missing links]() Collection index: [llms.txt]() Data updated: 2026-01-04T05:12:22.705Z Authors: Solenne Gaucher, Olga Klopp Published: 2021-11-05T07:43:14.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Link Prediction on Primary school network of interactions](): Link Prediction; Primary school network of interactions; Normalized Squared Frobenius Error: 0.312. - [Link Prediction on Network of co-authorship 892 nodes (50% missing values)](): Link Prediction; Network of co-authorship 892 nodes (50% missing values); Norm. Squared Frobenius Error: 0.857. ## Original sources and implementation [Original paper]() [PDF]()