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arXiv · 1802.07093

On the non-detectability of spiked large random tensors

Antoine Chevreuil·Philippe Loubaton
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Abstract

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 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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Antoine Chevreuil, Philippe Loubaton. 2018-02-20. On the non-detectability of spiked large random tensors. https://arxiv.org/abs/1802.07093

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