Statistical limits of spiked tensor models

@article{Perry2016StatisticalLO,
  title={Statistical limits of spiked tensor models},
  author={Amelia Perry and Alexander S. Wein and Afonso S. Bandeira},
  journal={CoRR},
  year={2016},
  volume={abs/1612.07728}
}
We study the statistical limits of both detecting and estimating a rank-one deformation of a symmetric random Gaussian tensor. We establish upper and lower bounds on the critical signal-to-noise ratio, under a variety of priors for the planted vector: (i) a uniformly sampled unit vector, (ii) i.i.d. ±1 entries, and (iii) a sparse vector where a constant fraction ρ of entries are i.i.d. ±1 and the rest are zero. For each of these cases, our upper and lower bounds match up to a 1+o(1) factor as… CONTINUE READING
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