Crossing the KS threshold in the stochastic block model with information theory

Emmanuel Abbe, Colin Sandon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Decelle et al. conjectured that community detection in the symmetric stochastic block model has a computational threshold given by the so-called Kesten-Stigum (KS) threshold, and that information-theoretic methods can cross this threshold for a large enough number of communities (4 or 5 depending on the regime of the parameters). This paper shows that at k = 5, it is possible to cross the KS threshold in the disassortative regime with a non-efficient algorithm that samples a clustering having typical cluster volumes. Further, the gap between the KS and information-theoretic threshold is shown to be large in some cases. In the case where edges are drawn only across clusters with an average degree of b, and denoting by k the number of communities, the KS threshold reads b ≳ k2 whereas our information-theoretic bound reads b ≳ k ln(k).

Original languageEnglish (US)
Title of host publicationProceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages840-844
Number of pages5
ISBN (Electronic)9781509018062
DOIs
StatePublished - Aug 10 2016
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: Jul 10 2016Jul 15 2016

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2016-August
ISSN (Print)2157-8095

Other

Other2016 IEEE International Symposium on Information Theory, ISIT 2016
CountrySpain
CityBarcelona
Period7/10/167/15/16

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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  • Cite this

    Abbe, E., & Sandon, C. (2016). Crossing the KS threshold in the stochastic block model with information theory. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory (pp. 840-844). [7541417] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541417