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2017 The Kato–Temple inequality and eigenvalue concentration with applications to graph inference
Joshua Cape, Minh Tang, Carey E. Priebe
Electron. J. Statist. 11(2): 3954-3978 (2017). DOI: 10.1214/17-EJS1328

Abstract

We present an adaptation of the Kato–Temple inequality for bounding perturbations of eigenvalues with applications to statistical inference for random graphs, specifically hypothesis testing and change-point detection. We obtain explicit high-probability bounds for the individual distances between certain signal eigenvalues of a graph’s adjacency matrix and the corresponding eigenvalues of the model’s edge probability matrix, even when the latter eigenvalues have multiplicity. Our results extend more broadly to the perturbation of singular values in the presence of quite general random matrix noise.

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Joshua Cape. Minh Tang. Carey E. Priebe. "The Kato–Temple inequality and eigenvalue concentration with applications to graph inference." Electron. J. Statist. 11 (2) 3954 - 3978, 2017. https://doi.org/10.1214/17-EJS1328

Information

Received: 1 August 2016; Published: 2017
First available in Project Euclid: 18 October 2017

zbMATH: 06796561
MathSciNet: MR3714304
Digital Object Identifier: 10.1214/17-EJS1328

Subjects:
Primary: 15A42, 62G15
Secondary: 05C80, 47A55

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Vol.11 • No. 2 • 2017
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