# Calibrating dependence between random elements

## TL;DR

This paper explores and refines measures of dependence between random variables, introducing a calibrated scale based on the complexity of approximating functions, building on classical concepts from Gebelein and Rényi.

## Contribution

It summarizes properties of Rényi's dependence measure and introduces a new calibrated scale based on function approximation complexity.

## Key findings

- Provides new properties of Rényi dependence measure
- Introduces a calibrated dependence scale
- Links dependence to function approximation complexity

## Abstract

Attempts to quantify dependence between random elements X and Y via maximal correlation go back to Gebelein (1941) and R\'{e}nyi (1959). After summarizing properties (including some new) of the R\'{e}nyi measure of dependence, a calibrated scale of dependence is introduced. It is based on the ``complexity`` of approximating functions of X by functions of Y.