Equivalence of concentration inequalities for linear and non-linear functions

Autor:	Sullivan, Timothy John, Owhadi, Houman
Rok vydání:	2010
Předmět:	Mathematics - Probability 60E15 60F10 52A07
Druh dokumentu:	Working Paper
Popis:	We consider a random variable $X$ that takes values in a (possibly infinite-dimensional) topological vector space $\mathcal{X}$. We show that, with respect to an appropriate "normal distance" on $\mathcal{X}$, concentration inequalities for linear and non-linear functions of $X$ are equivalent. This normal distance corresponds naturally to the concentration rate in classical concentration results such as Gaussian concentration and concentration on the Euclidean and Hamming cubes. Under suitable assumptions on the roundness of the sets of interest, the concentration inequalities so obtained are asymptotically optimal in the high-dimensional limit. Comment: 19 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1009.4913 Zobrazit plný text záznamu View this record from Arxiv