Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method

2019/02/19 by Barbier, Jean, Chan, Chun Lam, Macris, Nicolas
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Information Theory (cs.IT) #Probability (math.PR)

paper · doi:10.48550/arxiv.1902.07273

Abstract

We rigorously derive a single-letter variational expression for the mutual information of the asymmetric two-groups stochastic block model in the dense graph regime. Existing proofs in the literature are indirect, as they involve mapping the model to a rank-one matrix estimation problem whose mutual information is then determined by a combination of methods (e.g., interpolation, cavity, algorithmic, spatial coupling). In this contribution we provide a self-contained direct method using only the recently introduced adaptive interpolation method.

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