Testing Dependency of Weighted Random Graphs

Mor Oren-Loberman, Vered Paslev, Wasim Huleihel

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically independent, while under the alternative, the edges of one graph are dependent on the edges of a randomly vertex-permuted version of the other graph. For general edge-weights distributions, we establish thresholds at which optimal testing is information-theoretically impossible and possible, as a function of the total number of nodes in the observed graphs and the generative distributions of the weights. Finally, we observe a statistical-computational gap in our problem, and we provide evidence that this is fundamental using the framework of low-degree polynomials.

Original languageEnglish
Title of host publication2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1263-1268
Number of pages6
ISBN (Electronic)9798350382846
DOIs
StatePublished - 2024
Event2024 IEEE International Symposium on Information Theory, ISIT 2024 - Athens, Greece
Duration: 7 Jul 202412 Jul 2024

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2024 IEEE International Symposium on Information Theory, ISIT 2024
Country/TerritoryGreece
CityAthens
Period7/07/2412/07/24

Funding

FundersFunder number
Israel Science Foundation1734/21

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