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Mean-field variational inference (MFVI) has been widely applied in largescale Bayesian inference. However MFVI, which assumes a product distribution onthe latent variables, often leads to objective functions with many localoptima, making optimization algorithms sensitive to initialization. In thispaper, we study the advantage of structured variational inference for the twoclass Stochastic Blockmodel. The variational distribution is constructed tohave pairwise dependency structure on the nodes of the network. We prove that,in a broad density regime and for general random initializations, unlike MFVI,the class labels estimated from our method converge to the ground truth withhigh probability, when the model parameters are known, estimated within areasonable range or jointly optimized with the variational parameters. Inaddition, empirically we demonstrate structured VI is more robust compared withMFVI when the graph is sparse and the signal to noise ratio is low. The papertakes a first step towards understanding the importance of dependency structurein variational inference for community detection.

A Theoretical Case Study of Structured Variational Inference for Community Detection