On The Non-Detectability of Spiked Large Random Tensors

@article{Chevreuil2018OnTN,
  title={On The Non-Detectability of Spiked Large Random Tensors},
  author={Antoine Chevreuil and Philippe Loubaton},
  journal={2018 IEEE Statistical Signal Processing Workshop (SSP)},
  year={2018},
  pages={443-447}
}
  • A. Chevreuil, P. Loubaton
  • Published 20 February 2018
  • Mathematics, Computer Science, Engineering
  • 2018 IEEE Statistical Signal Processing Workshop (SSP)
This paper addresses the detection of a low rank high-dimensional tensor corrupted by an additive complex Gaussian noise. In the asymptotic regime where all the dimensions of the tensor converge towards $+\infty $ 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… Expand
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