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dc.contributor.authorBangachev, Kiril
dc.contributor.authorBresler, Guy
dc.date.accessioned2024-07-10T18:53:28Z
dc.date.available2024-07-10T18:53:28Z
dc.date.issued2024-06-10
dc.identifier.isbn979-8-4007-0383-6
dc.identifier.urihttps://hdl.handle.net/1721.1/155580
dc.descriptionSTOC ’24, June 24–28, 2024, Vancouver, BC, Canadaen_US
dc.description.abstractThe random geometric graph RGG(n,Sd−1,p) is formed by sampling n i.i.d. vectors {Vi}i = 1n uniformly on Sd−1 and placing an edge between pairs of vertices i and j for which ⟨ Vi,Vj⟩ ≥ τdp, where τdp is such that the expected density is p. We study the low-degree Fourier coefficients of the distribution RGG(n,Sd−1,p) and its Gaussian analogue. Our main conceptual contribution is a novel two-step strategy for bounding Fourier coefficients which we believe is more widely applicable to studying latent space distributions. First, we localize the dependence among edges to few fragile edges. Second, we partition the space of latent vector configurations (Sd−1)⊗ n based on the set of fragile edges and on each subset of configurations, we define a noise operator acting independently on edges not incident (in an appropriate sense) to fragile edges. We apply the resulting bounds to: 1) Settle the low-degree polynomial complexity of distinguishing spherical and Gaussian random geometric graphs from Erdos-Renyi both in the case of observing a complete set of edges and in the non-adaptively chosen mask M model recently introduced by Mardia, Verchand, and Wein; 2) Exhibit a statistical-computational gap for distinguishing RGG and a planted coloring model in a regime when RGG is distinguishable from ; 3) Reprove known bounds on the second eigenvalue of ren_US
dc.publisherACMen_US
dc.relation.isversionof10.1145/3618260.3649676en_US
dc.rightsCreative Commons Attributionen_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.sourceAssociation for Computing Machineryen_US
dc.titleOn the Fourier Coefficients of High-Dimensional Random Geometric Graphsen_US
dc.typeArticleen_US
dc.identifier.citationBangachev, Kiril and Bresler, Guy. 2024. "On the Fourier Coefficients of High-Dimensional Random Geometric Graphs."
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
dc.identifier.mitlicensePUBLISHER_CC
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2024-07-01T07:49:16Z
dc.language.rfc3066en
dc.rights.holderThe author(s)
dspace.date.submission2024-07-01T07:49:17Z
mit.licensePUBLISHER_CC
mit.metadata.statusAuthority Work and Publication Information Neededen_US


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