Information Theoretic Limits of Exact Recovery in Sub-hypergraph Models for Community Detection

In this paper, we study the information theoretic bounds for exact recovery in sub-hypergraph models for community detection. We define a general model called the m-uniform sub-hypergraph stochastic block model (m-ShSBM). Under the m-ShSBM, we use Fano's inequality to identify the region of model parameters where any algorithm fails to exactly recover the planted communities with a large probability. We also identify the region where a Maximum Likelihood Estimation (MLE) algorithm succeeds to exactly recover the communities with high probability. Our bounds are tight up to a log(k) term and pertain to the community detection problems in various models such as the planted hypergraph stochastic block model, the planted densest sub-hypergraph model, and the planted multipartite hypergraph model.