Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approach
Probability
2018-07-10 v1 Information Theory
Machine Learning
math.IT
Abstract
We study the problem of community detection in a random hypergraph model which we call the stochastic block model for -uniform hypergraphs (-SBM). We investigate the exact recovery problem in -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.
Cite
@article{arxiv.1807.02884,
title = {Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approach},
author = {Chiheon Kim and Afonso S. Bandeira and Michel X. Goemans},
journal= {arXiv preprint arXiv:1807.02884},
year = {2018}
}