On Concentration Inequalities for Vector-Valued Lipschitz Functions

TL;DR

This paper develops new concentration inequalities for vector-valued Lipschitz functions, providing potentially tighter bounds on deviation probabilities than classical results, which can improve analysis in high-dimensional probability and statistics.

Contribution

It introduces two novel upper bounds for deviation probabilities of vector-valued Lipschitz functions, enhancing existing concentration inequality techniques.

Findings

Derived two upper bounds for deviation probabilities.

Bounds can be tighter than classical inequalities.

Applicable to high-dimensional probabilistic analysis.

Abstract

We derive two upper bounds for the probability of deviation of a vector-valued Lipschitz function of a collection of random variables from its expected value. The resulting upper bounds can be tighter than bounds obtained by a direct application of a classical theorem due to Bobkov and G\"{o}tze.