Robust recovery of low-rank matrices and low-tubal-rank tensors from noisy sketches

TL;DR

This paper provides theoretical guarantees for recovering low-rank matrices and tensors from noisy sketches using double sketching, advancing understanding of its accuracy and robustness in large-scale data compression.

Contribution

It introduces the first theoretical error bounds for double sketching in low-rank matrix and tensor recovery, based on non-asymptotic random matrix theory.

Findings

Error bounds for matrix recovery from noisy sketches

Application to low-rank matrix approximation

Extension to low-tubal-rank tensor recovery

Abstract

A common approach for compressing large-scale data is through matrix sketching. In this work, we consider the problem of recovering low-rank matrices from two noisy linear sketches using the double sketching scheme discussed in Fazel et al. (2008), which is based on an approach by Woolfe et al. (2008). Using tools from non-asymptotic random matrix theory, we provide the first theoretical guarantees characterizing the error between the output of the double sketch algorithm and the ground truth low-rank matrix. We apply our result to the problems of low-rank matrix approximation and low-tubal-rank tensor recovery.