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Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approach (1807.02884v1)
Published 8 Jul 2018 in math.PR, cs.IT, cs.LG, and math.IT
Abstract: 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.