Abstract
The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in order to succeed with efficient algorithms in the challenging cases where the local structure of the graph is homogeneous. This paper provides an efficient algorithm to learn graphons in the constant expected degree regime. The algorithm is shown to succeed in estimating the rank-k projection of a graphon in the metric if the top k eigenvalues of the graphon satisfy a generalized Kesten–Stigum condition.
Funding Statement
The first author was supported by the NSF CAREER Award CCF-1552131. The third author is supported by NSF Grants DMS-1855527, DMS-1749103, a Simons Investigator grant, and a MacArthur Fellowship.
Acknowledgments
The authors would like to thank the Editors and the anonymous referees for their constructive comments that improved the quality of this paper.
Citation
Emmanuel Abbe. Shuangping Li. Allan Sly. "Learning sparse graphons and the generalized Kesten–Stigum threshold." Ann. Statist. 51 (2) 599 - 623, April 2023. https://doi.org/10.1214/23-AOS2262
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