Corpus ID: 2695583

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={E. Abbe and Colin Sandon},
  journal={ArXiv},
  year={2015},
  volume={abs/1512.09080}
}
  • E. Abbe, Colin Sandon
  • Published 2015
  • Mathematics, Computer Science
  • ArXiv
  • In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed by Mossel et al., made the following conjecture: Denote by $k$ the number of balanced communities, $a/n$ the probability of connecting inside communities and $b/n$ across, and set $\mathrm{SNR}=(a-b)^2/(k(a+(k-1)b)$; for any $k \geq 2$, it is possible to detect communities efficiently whenever $\mathrm{SNR}>1$ (the KS threshold), whereas for $k\geq 4$, it is possible to detect communities… CONTINUE READING
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