Sharp Concentration of Simple Random Tensors

TL;DR

This paper develops precise, dimension-free concentration inequalities for sums of simple random tensors, extending classical empirical process results to higher-order tensor settings using generic chaining techniques.

Contribution

It introduces sharp concentration bounds for simple random tensors and generalizes empirical process inequalities to higher-order tensor contexts.

Findings

Dimension-free concentration inequalities established

Sharp high-probability bounds derived for tensor sums

Generalization of classical empirical process results

Abstract

This paper establishes sharp dimension-free concentration inequalities and expectation bounds for the deviation of the sum of simple random tensors from its expectation. As part of our analysis, we use generic chaining techniques to obtain a sharp high-probability upper bound on the suprema of $L_p$ empirical processes. In so doing, we generalize classical results for quadratic and product empirical processes to higher-order settings.