Belief propagation, robust reconstruction and optimal recovery of block models

@inproceedings{Mossel2014BeliefPR,
  title={Belief propagation, robust reconstruction and optimal recovery of block models},
  author={Elchanan Mossel and Joe Neeman and Allan Sly},
  booktitle={COLT},
  year={2014}
}
We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities a=n and b=n for inter- and intra-block edge probabilities respectively. It was recently shown that one can do better than a random guess if and only if (a b) 2 > 2(a + b). Using a variant of Belief Propagation, we give a reconstruction algorithm that is optimal in the sense that if (a b) 2 > C(a + b) for some constant C then our algorithm maximizes the fraction of the nodes… 

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