Tail bounds via generic chaining
Probability
2014-03-25 v2 Information Theory
math.IT
Abstract
We modify Talagrand's generic chaining method to obtain upper bounds for all p-th moments of the supremum of a stochastic process. These bounds lead to an estimate for the upper tail of the supremum with optimal deviation parameters. We apply our procedure to improve and extend some known deviation inequalities for suprema of unbounded empirical processes and chaos processes. As an application we give a significantly simplified proof of the restricted isometry property of the subsampled discrete Fourier transform.
Cite
@article{arxiv.1309.3522,
title = {Tail bounds via generic chaining},
author = {Sjoerd Dirksen},
journal= {arXiv preprint arXiv:1309.3522},
year = {2014}
}
Comments
Added detailed proof of Theorem 3.5; Application to dimensionality reduction expanded and moved to separate note arXiv:1402.3973