| Paper ID | D6-S2-T3.2 |
| Paper Title |
Information Theoretic Limits of Exact Recovery in Sub-hypergraph Models for Community Detection |
| Authors |
Jiajun Liang, Chuyang Ke, Jean Honorio, Purdue University, United States |
| Session |
D6-S2-T3: Sub-Hypergraph Models |
| Chaired Session: |
Monday, 19 July, 22:20 - 22:40 |
| Engagement Session: |
Monday, 19 July, 22:40 - 23:00 |
| Abstract |
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.
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