# Local Lift Dependence Scale

## TL;DR

This paper introduces the Local Lift Dependence Scale, a versatile and general measure of dependence between two random variables that surpasses traditional coefficients like Mutual Information in flexibility and applicability.

## Contribution

The paper presents a novel local dependence quantifier that does not assume specific dependence forms and applies to a broad class of random variables, including singular and absolutely continuous types.

## Key findings

- Proposes the Local Lift Dependence Scale as a new dependence measure.
- Demonstrates the scale's generality over existing measures like Mutual Information.
- Discusses potential applications and future research directions.

## Abstract

We propose a local and general dependence quantifier between two random variables $X$ and $Y$, which we call Local Lift Dependence Scale, that does not assume any form of dependence (e.g., linear) between $X$ and $Y$, and is defined for a large class of random variables, singular and absolutely continuous w.r.t Lebesgue measure. We argue that this dependence scale is more general and suitable to study variable dependence than other specific local dependence quantifiers and global dependence coefficients, as the Mutual Information. An outline of how this dependence scale may be useful in branches of applied probability and topics for future research are presented.