On the Accuracy of Hotelling-Type Asymmetric Tensor Deflation: A Random
  Tensor Analysis
Mohamed El Amine Seddik Maxime Guillaud Alexis Decurninge José Henrique de Morais Goulart
This work introduces an asymptotic study of Hotelling-type tensor deflation
in the presence of noise, in the regime of large tensor dimensions.
Specifically, we consider a low-rank asymmetric tensor model of the form
$\sum_{i=1}^r \beta_i{\mathcal{A}}_i + {\mathcal{W}}$ where $\beta_i\geq 0$ and
the ${\mathcal{A}}_i$'s are unit-norm rank-one tensors such that $\left|
\langle {\mathcal{A}}_i, {\mathcal{A}}_j \rangle \right| \in [0, 1]$ for $i\neq
j$ and ${\mathcal{W}}$ is an additive noise term. Assuming that the dominant
components are successively estimated from the noisy observation and
subsequently subtracted, we leverage recent advances in random tensor theory in
the regime of asymptotically large tensor dimensions to analytically
characterize the estimated singular values and the alignment of estimated and
true singular vectors at each step of the deflation procedure. Furthermore,
this result can be used to construct estimators of the signal-to-noise ratios
$\beta_i$ and the alignments between the estimated and true rank-1 signal
components.