Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squares

TL;DR

This paper explores community detection in hypergraphs using spiked tensor models, revealing differences in computational and statistical limits compared to matrix models, and evaluates Sum-of-Squares algorithms' effectiveness.

Contribution

It introduces a novel spiked tensor model for hypergraph community detection and compares its computational-statistical gap with related matrix models.

Findings

Sum-of-Squares algorithms perform differently on hypergraph models.

The hypergraph model exhibits a larger computational-statistical gap.

Distinct behaviors between tensor and matrix models in community detection.

Abstract

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.