Accelerating ILL-Conditioned Robust Low-Rank Tensor Regression

Tian Tong; Cong Ma; Yuejie Chi

ICASSP 2022accepted0 citations

Accelerating ILL-Conditioned Robust Low-Rank Tensor Regression

Abstract

An important problem that arises across different applications in signal processing, machine learning, and data science is to reliably estimate a tensor from a small number of measurements that are possibly corrupted. Leveraging the low-rank structure under the Tucker decomposition, we propose a provably efficient algorithm that directly estimates the tensor factors by solving a nonsmooth and nonconvex composite optimization problem that minimizes the least absolute deviation loss. The proposed algorithm—built on subgradient methods—harnesses preconditioners that are designed to be equivariant w.r.t. the low-rank parameterization, and is shown to achieve local linear convergence at a constant rate under the Gaussian design. Numerical experiments are provided to corroborate the superior performance of the proposed algorithm.

BibTeX

@inproceedings{icassp2022_acceleratingillc,
  title = {Accelerating ILL-Conditioned Robust Low-Rank Tensor Regression},
  author = {Tian Tong and Cong Ma and Yuejie Chi},
  booktitle = {ICASSP 2022},
  year = {2022}
}