The Landscape of the Spiked Tensor Model

We consider the problem of estimating a large rank‐one tensor u⊗k ∈ (ℝn)⊗k, k ≥ 3, in Gaussian noise. Earlier work characterized a critical signal‐to‐noise ratio λ  Bayes = O(1) above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably, no...

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Bibliographic Details

Published in:	Communications on pure and applied mathematics Vol. 72; no. 11; pp. 2282 - 2330
Main Authors:	Arous, Gérard Ben, Mei, Song, Montanari, Andrea, Nica, Mihai
Format:	Journal Article
Language:	English
Published:	Melbourne John Wiley & Sons Australia, Ltd 01.11.2019 John Wiley and Sons, Limited
Subjects:	Algorithms Critical point Economic models Mathematical analysis Maxima Maximum likelihood estimators Optimization Polynomials Random noise Semidefinite programming Tensors
ISSN:	0010-3640, 1097-0312
Online Access:	Get full text
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