A Rank Minrelation - Majrelation Coefficient

TL;DR

This paper introduces the rank minrelation coefficient, a new statistical measure for detecting asymmetric dependencies between variables, which can improve variable selection and network inference.

Contribution

The paper proposes a novel bivariate dependency measure called the rank minrelation coefficient, focusing on asymmetric relationships and demonstrating its advantages over correlation.

Findings

The new coefficient effectively detects asymmetric variable dependencies.

It outperforms correlation in variable selection tasks.

The measure captures directional relationships between continuous variables.

Abstract

Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank minrelation coefficient. We define a minrelation of X to Y (or equivalently a majrelation of Y to X) as a measure that estimate p(Y > X) when X and Y are continuous random variables. The approach is similar to Lin's concordance coefficient that rather focuses on estimating p(X = Y). In other words, if a variable X exhibits a minrelation to Y then, as X increases, Y is likely to increases too. However, on the contrary to concordance or correlation, the minrelation is not symmetric. More explicitly, if X decreases, little can be said on Y values (except that the uncertainty on Y actually increases). In this paper, we formally define this new kind of bivariate dependencies and propose a new statistical coefficient in order to detect those dependencies. We show through several key examples that this new coefficient has many interesting properties in order to select relevant variables, in particular when compared to correlation.