Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gap

@article{Abbe2015DetectionIT,
  title={Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gap},
  author={Emmanuel Abbe and Colin Sandon},
  journal={CoRR},
  year={2015},
  volume={abs/1512.09080}
}
In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed up Mossel et al., made a fascinating conjecture: Denote by k the number of balanced communities, a/n the probability of connecting inside communities and b/n across, and set SNR = |a− b|/ √ k(a+ (k − 1)b); for any k ≥ 2, it is possible to detect communities efficiently whenever SNR > 1 (the KS threshold), whereas for k ≥ 5, it is possible to detect communities information-theoretically for some SNR… CONTINUE READING
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