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On the non-detectability of spiked large random tensors

Abstract : This paper addresses the detection of a low rank high-dimensional tensor (spike) of order larger than 3, corrupted by an additive complex Gaussian noise. In the asymptotic regime where all the dimensions of the tensor converge towards infinity at the same rate, existing results devoted to rank 1 tensors are extended. It is proved that if a certain parameter depending explicitly on the low rank tensor is below a threshold, then the null hypothesis and the presence of the low rank tensor are undistinguishable hypotheses in the sense that no test performs better than a random choice.
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https://hal.archives-ouvertes.fr/hal-01798509
Contributor : Antoine Chevreuil <>
Submitted on : Wednesday, May 23, 2018 - 3:21:13 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:07 PM
Document(s) archivé(s) le : Friday, August 24, 2018 - 10:10:50 PM

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  • HAL Id : hal-01798509, version 1

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Antoine Chevreuil, Philippe Loubaton. On the non-detectability of spiked large random tensors . SSP, Jun 2018, Freiburg, Germany. ⟨hal-01798509⟩

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