On the non-detectability of spiked large random tensors

2018/02/20 by Chevreuil, Antoine, Loubaton, Philippe
#FOS: Electrical engineering #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.1802.07093

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 +∞ 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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