We study the problem of community detection in hypergraphs under a stochastic
block model. Similarly to how the stochastic block model in graphs suggests
studying spiked random matrices, our model motivates investigating statistical
and computational limits of exact recovery in a certain spiked tensor model. In
contrast with the matrix case, the spiked model naturally arising from
community detection in hypergraphs is different from the one arising in the
so-called tensor Principal Component Analysis model. We investigate the
effectiveness of algorithms in the Sum-of-Squares hierarchy on these models.
Interestingly, our results suggest that these two apparently similar models
exhibit significantly different computational to statistical gaps.Comment: In proceedings of 2017 International Conference on Sampling Theory
and Applications (SampTA
