# A Bernstein Inequality For Exponentially Growing Graphs

## TL;DR

This paper introduces a Bernstein inequality tailored for sums of random variables on exponentially growing graphs, enabling better concentration bounds in highly-connected network structures.

## Contribution

It provides a novel Bernstein inequality applicable to graphs with exponential node growth, aiding in statistical analysis of complex networks.

## Key findings

- Derived a Bernstein inequality for exponential graphs
- Facilitates concentration inequalities in highly-connected networks
- Supports consistency analysis of nonparametric estimators

## Abstract

In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in highly-connected networks. It can be useful to obtain consistency properties for nonparametric estimators of conditional expectation functions which are derived from such networks.