The Randomized Dependence Coefficient

TL;DR

The paper presents the Randomized Dependence Coefficient (RDC), a computationally efficient measure of non-linear dependence between variables, invariant to marginal transformations, and easy to implement.

Contribution

It introduces RDC, a novel dependence measure based on randomized projections of copulas, offering simplicity, invariance, and low computational cost.

Findings

RDC effectively captures non-linear dependence.

RDC is invariant under marginal transformations.

RDC is easy to implement in just five lines of R code.

Abstract

We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-R\'enyi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respect to marginal distribution transformations, has low computational cost and is easy to implement: just five lines of R code, included at the end of the paper.