The Hypergraph Stochastic Block Model (HSBM) is a complex, many-parameter model generalizing the well-known graph SBM--a paradigm for studying community detection. One of the main uses of the (H)SBM is that it allows us to develop guarantees for community detection algorithms by providing thresholds---parameter conditions that theoretically describe the necessary and sufficient requirements for community detection in the model. These thresholds naturally depend on the type of recovery desired.

I will talk about the most general conditions and thresholds we can develop, under various tweaks in the model, for almost exact and exact recovery in more, or less, general HSBM. This is joint work with Haixiao Wang and Yizhe Zhu.