Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approach

07/08/2018

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by   Chiheon Kim, et al.

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We study the problem of community detection in a random hypergraph model which we call the stochastic block model for k-uniform hypergraphs (k-SBM). We investigate the exact recovery problem in k-SBM and show that a sharp phase transition occurs around a threshold: below the threshold it is impossible to recover the communities with non-vanishing probability, yet above the threshold there is an estimator which recovers the communities almost asymptotically surely. We also consider a simple, efficient algorithm for the exact recovery problem which is based on a semidefinite relaxation technique.