# Copula Correlation: An Equitable Dependence Measure and Extension of Pearson's Correlation

arXiv: https://arxiv.org/abs/1312.7214 · HTML: https://mlsanity.com/paper/1312.7214/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2013.

## Built on by (most cited first, 1 of 1)

- [A Copula Based Supervised Filter for Feature Selection in Diabetes Risk Prediction Using Machine Learning](https://mlsanity.com/paper/2505.22554/) (2025)

## Abstract (arXiv)

In Science, Reshef et al. (2011) proposed the concept of equitability for measures of dependence between two random variables. To this end, they proposed a novel measure, the maximal information coefficient (MIC). Recently a PNAS paper (Kinney and Atwal, 2014) gave a mathematical definition for equitability. They proved that MIC in fact is not equitable, while a fundamental information theoretic measure, the mutual information (MI), is self-equitable. In this paper, we show that MI also does not correctly reflect the proportion of deterministic signals hidden in noisy data. We propose a new equitability definition based on this scenario. The copula correlation (Ccor), based on the L1-distance of copula density, is shown to be equitable under both definitions. We also prove theoretically that Ccor is much easier to estimate than MI. Numerical studies illustrate the properties of the measures.