Testing for high-dimensional geometry in random graphs
Author(s): Bubeck, Sébastien; Ding, Jian; Eldan, Ronen; Rácz, Miklós Z
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Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Bubeck, Sébastien | - |
dc.contributor.author | Ding, Jian | - |
dc.contributor.author | Eldan, Ronen | - |
dc.contributor.author | Rácz, Miklós Z | - |
dc.date.accessioned | 2021-10-11T14:17:55Z | - |
dc.date.available | 2021-10-11T14:17:55Z | - |
dc.date.issued | 2016-10 | en_US |
dc.identifier.citation | Bubeck, Sébastien, Ding, Jian, Eldan, Ronen, Rácz, Miklós Z. (2016). Testing for high-dimensional geometry in random graphs. Random Structures & Algorithms, 49 (3), 503 - 532. doi:10.1002/rsa.20633 | en_US |
dc.identifier.issn | 1042-9832 | - |
dc.identifier.uri | http://arks.princeton.edu/ark:/88435/pr19p3n | - |
dc.description.abstract | We study the problem of detecting the presence of an underlying high-dimensional geometric structure in a random graph. Under the null hypothesis, the observed graph is a realization of an Erdős-Rényi random graph G(n,p). Under the alternative, the graph is generated from the G(n,p,d) model, where each vertex corresponds to a latent independent random vector uniformly distributed on the sphere Sd−1, and two vertices are connected if the corresponding latent vectors are close enough. In the dense regime (i.e., p is a constant), we propose a near-optimal and computationally efficient testing procedure based on a new quantity which we call signed triangles. The proof of the detection lower bound is based on a new bound on the total variation distance between a Wishart matrix and an appropriately normalized GOE matrix. In the sparse regime, we make a conjecture for the optimal detection boundary. We conclude the paper with some preliminary steps on the problem of estimating the dimension in G(n,p,d). | en_US |
dc.format.extent | 503 - 532 | en_US |
dc.language.iso | en_US | en_US |
dc.relation.ispartof | Random Structures & Algorithms | en_US |
dc.rights | Author's manuscript | en_US |
dc.title | Testing for high-dimensional geometry in random graphs | en_US |
dc.type | Journal Article | en_US |
dc.identifier.doi | doi:10.1002/rsa.20633 | - |
dc.date.eissued | 2016-01-06 | en_US |
pu.type.symplectic | http://www.symplectic.co.uk/publications/atom-terms/1.0/journal-article | en_US |
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