The Landscape of the Spiked Tensor Model

Communications on Pure and Applied Mathematics, pp. 2282-2330, 2019.

Cited by: 4|Bibtex|Views13|

Abstract:

We consider the problem of estimating a large rank-one tensor ${boldsymbol u}^{otimes k}in({mathbb R}^{n})^{otimes k}$, $kge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $lambda_{Bayes}= O(1)$ above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Rem...More

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