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

arXiv: https://arxiv.org/abs/2211.09004 · HTML: https://mlsanity.com/paper/2211.09004/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 14 references that are in the map.
- First posted on arXiv 16 Nov 2022.

## 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)
- [On Estimating Rank-One Spiked Tensors in the Presence of Heavy Tailed Errors](https://mlsanity.com/paper/2107.09660/) (2021)
- [Long Random Matrices and Tensor Unfolding](https://mlsanity.com/paper/2110.10210/) (2021)
- [When Random Tensors meet Random Matrices](https://mlsanity.com/paper/2112.12348/) (2021)

## Built on by (most cited first, 1 of 1)

- [Optimizing Orthogonalized Tensor Deflation via Random Tensor Theory](https://mlsanity.com/paper/2302.05798/) (2023)

## Abstract (arXiv)

Leveraging on recent advances in random tensor theory, we consider in this paper a rank-r asymmetric spiked tensor model of the form sumi=1r βi Ai + W where βi≥ 0 and the Ai's are rank-one tensors such that langle Ai, Aj rangle∈ [0, 1] for ineq j, based on which we provide an asymptotic study of Hotelling-type tensor deflation in the large dimensional regime. Specifically, our analysis characterizes the singular values and alignments at each step of the deflation procedure, for asymptotically large tensor dimensions. This can be used to construct consistent estimators of different quantities involved in the underlying problem, such as the signal-to-noise ratios βi or the alignments between the different signal components langle Ai, Aj rangle.