Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method
Information Theory
2019-07-17 v2 Disordered Systems and Neural Networks
math.IT
Probability
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.
Keywords
Cite
@article{arxiv.1902.07273,
title = {Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method},
author = {Jean Barbier and Chun Lam Chan and Nicolas Macris},
journal= {arXiv preprint arXiv:1902.07273},
year = {2019}
}