Mathematics – Probability
Scientific paper
2010-09-24
Mathematics
Probability
19 pages, 5 figures
Scientific paper
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.
Owhadi Houman
Sullivan Timothy John
No associations
LandOfFree
Equivalence of concentration inequalities for linear and non-linear functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Equivalence of concentration inequalities for linear and non-linear functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equivalence of concentration inequalities for linear and non-linear functions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-275634