On the Dimension-Free Concentration of Simple Tensors via Matrix Deviation

TL;DR

This paper offers a simplified proof of a sharp concentration inequality for subgaussian simple tensors, utilizing matrix deviation inequalities and chaining techniques to improve understanding of tensor concentration phenomena.

Contribution

The paper introduces a more straightforward proof method for tensor concentration inequalities, enhancing theoretical clarity and accessibility.

Findings

Provides a simpler proof of tensor concentration inequality

Uses matrix deviation inequalities for  norms

Employs chaining argument for the proof

Abstract

We provide a simpler proof of a sharp concentration inequality for subgaussian simple tensors obtained recently by Al-Ghattas, Chen and Sanz-Alonso. Our approach uses a matrix deviation inequality for $\ell^p$ norms and a basic chaining argument.