Equitability of Dependence Measure

TL;DR

This paper introduces a new definition of equitability for dependence measures, emphasizing the importance of consistent scoring across different types of relationships, and evaluates existing measures under this framework.

Contribution

It proposes a novel concept of weak-equitability for dependence measures and demonstrates that HHG and CDC satisfy this property through simulations.

Findings

HHG and CDC are weak-equitable dependence measures.

The paper provides a new framework for assessing dependence measure equitability.

Simulations support the proposed definition and evaluation criteria.

Abstract

Measuring dependence between two random variables is very important, and critical in many applied areas such as variable selection, brain network analysis. However, we do not know what kind of functional relationship is between two covariates, which requires the dependence measure to be equitable. That is, it gives similar scores to equally noisy relationship of different types. In fact, the dependence score is a continuous random variable taking values in $[0,1]$, thus it is theoretically impossible to give similar scores. In this paper, we introduce a new definition of equitability of a dependence measure, i.e, power-equitable (weak-equitable) and show by simulation that HHG and Copula Dependence Coefficient (CDC) are weak-equitable.