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 title: Thresholds for Reconstruction of Random Hypergraphs From Graph Projections
 section: Original Papers
-abstract: 'The graph projection of a hypergraph is a simple graph with the same vertex set and with an edge between each pair of vertices that appear in a hyperedge. We consider the problem of reconstructing a random d-uniform hypergraph from its projection. Feasibility of this task depends on d and the density of hyperedges in the random hypergraph. For $d =3$ we precisely determine the threshold, while for $d\ge 4$ we give bounds. All of our feasibility results are obtained by exhibiting an efficient algorithm for reconstructing the original hypergraph, while infeasibility is information-theoretic. Our results also apply to mildly inhomogeneous random hypergrahps, including hypergraph stochastic block models (HSBM). A consequence of our results is an optimal HSBM recovery algorithm, improving on Gaudio and Joshi (2023a). '
+abstract: 'The graph projection of a hypergraph is a simple graph with the same vertex set and with an edge between each pair of vertices that appear in a hyperedge. We consider the problem of reconstructing a random $d$-uniform hypergraph from its projection. Feasibility of this task depends on $d$ and the density of hyperedges in the random hypergraph. For $d=3$ we precisely determine the threshold, while for $d\ge 4$ we give bounds. All of our feasibility results are obtained by exhibiting an efficient algorithm for reconstructing the original hypergraph, while infeasibility is information-theoretic. Our results also apply to mildly inhomogeneous random hypergrahps, including hypergraph stochastic block models (HSBM). A consequence of our results is an optimal HSBM recovery algorithm, improving on Gaudio and Joshi (2023a). '
 layout: inproceedings
 series: Proceedings of Machine Learning Research
 publisher: PMLR