diff --git a/_posts/2024-06-30-bresler24a.md b/_posts/2024-06-30-bresler24a.md index b180580..310187f 100644 --- a/_posts/2024-06-30-bresler24a.md +++ b/_posts/2024-06-30-bresler24a.md @@ -1,16 +1,7 @@ --- 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 $d\geq 4$ 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. A consequence of our - results is that claims from the 2023 COLT paper gaudio’23 are disproved. ' +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