Exact Recovery of Community Detection in dependent Gaussian Mixture Models

We study the community detection problem on a Gaussian mixture model, in which (1) vertices are divided into \(k\geq 2\) distinct communities that are not necessarily equally-sized; (2) the Gaussian perturbations for different entries in the observation matrix are not necessarily independent or iden...

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Bibliographic Details
Published inarXiv.org
Main Authors Li, Zhongyang, Yang, Sichen
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.09.2022
Subjects
Apexes
Maximum likelihood estimation
Mixtures
Perturbation
Probabilistic models
Random variables
Recovery
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Summary:We study the community detection problem on a Gaussian mixture model, in which (1) vertices are divided into \(k\geq 2\) distinct communities that are not necessarily equally-sized; (2) the Gaussian perturbations for different entries in the observation matrix are not necessarily independent or identically distributed. We prove necessary and sufficient conditions for the exact recovery of the maximum likelihood estimation (MLE), and discuss the cases when these necessary and sufficient conditions give sharp threshold. Applications include the community detection on a graph where the Gaussian perturbations of observations on each edge is the sum of i.i.d.~Gaussian random variables on its end vertices, in which we explicitly obtain the threshold for the exact recovery of the MLE.
ISSN:2331-8422