# A Bernstein-type inequality for functions of bounded interaction

## TL;DR

This paper introduces a Bernstein-type concentration inequality for functions of independent variables with bounded interaction, extending classical bounds to more complex functions and improving results for U-statistics and regularized least squares.

## Contribution

It provides a new distribution-dependent concentration inequality that generalizes Bernstein's inequality to functions with limited interaction among variables.

## Key findings

- Sharper bounds for U-statistics
- Improved generalization error estimates for regularized least squares
- Extension of Bernstein's inequality to complex functions

## Abstract

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the other arguments. Applications sharpen existing bounds for U-statistics and the generalization error of regularized least squares.