# On the Accuracy of Hotelling-Type Asymmetric Tensor Deflation: A Random Tensor Analysis

arXiv: https://arxiv.org/abs/2310.18717 · HTML: https://mlsanity.com/paper/2310.18717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 28 Oct 2023.

## Builds on (most cited first, 6 of 6)

- [A statistical model for tensor PCA](https://mlsanity.com/paper/1411.1076/) (2014)
- [Statistical limits of spiked tensor models](https://mlsanity.com/paper/1612.07728/) (2016)
- [A Random Matrix Perspective on Random Tensors](https://mlsanity.com/paper/2108.00774/) (2021)
- [Long Random Matrices and Tensor Unfolding](https://mlsanity.com/paper/2110.10210/) (2021)
- [On Estimating Rank-One Spiked Tensors in the Presence of Heavy Tailed Errors](https://mlsanity.com/paper/2107.09660/) (2021)
- [When Random Tensors meet Random Matrices](https://mlsanity.com/paper/2112.12348/) (2021)

## Abstract (arXiv)

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 sumi=1r βiAi + W where βi≥ 0 and the Ai's are unit-norm rank-one tensors such that left| langle Ai, Aj rangle right| ∈ [0, 1] for ineq j and 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 βi and the alignments between the estimated and true rank-1 signal components.