Sharp Concentration of Simple Random Tensors
Probability
2025-09-30 v2 Statistics Theory
Statistics Theory
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 empirical processes. In so doing, we generalize classical results for quadratic and product empirical processes to higher-order settings.
Cite
@article{arxiv.2502.16916,
title = {Sharp Concentration of Simple Random Tensors},
author = {Omar Al-Ghattas and Jiaheng Chen and Daniel Sanz-Alonso},
journal= {arXiv preprint arXiv:2502.16916},
year = {2025}
}
Comments
36 pages, minor revision, to appear in Information and Inference