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August 2020 Statistical thresholds for tensor PCA
Aukosh Jagannath, Patrick Lopatto, Léo Miolane
Ann. Appl. Probab. 30(4): 1910-1933 (August 2020). DOI: 10.1214/19-AAP1547

Abstract

We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor. We compute the sharp thresholds for hypothesis testing and estimation by maximum likelihood and show that they are the same. Furthermore, we find that the maximum likelihood estimator achieves the maximal correlation with the planted vector among measurable estimators above the estimation threshold. In this setting, the maximum likelihood estimator exhibits a discontinuous BBP-type transition: below the critical threshold the estimator is orthogonal to the planted vector, but above the critical threshold, it achieves positive correlation which is uniformly bounded away from zero.

Citation

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Aukosh Jagannath. Patrick Lopatto. Léo Miolane. "Statistical thresholds for tensor PCA." Ann. Appl. Probab. 30 (4) 1910 - 1933, August 2020. https://doi.org/10.1214/19-AAP1547

Information

Received: 1 December 2018; Revised: 1 July 2019; Published: August 2020
First available in Project Euclid: 4 August 2020

MathSciNet: MR4132641
Digital Object Identifier: 10.1214/19-AAP1547

Subjects:
Primary: 62F05, 62F10, 82B26, 82D30

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 4 • August 2020
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