The BP Dependency Function: a Generic Measure of Dependence between Random Variables

TL;DR

This paper introduces a new, comprehensive dependency function for random variables that overcomes the limitations of Pearson correlation, providing a more general measure of dependence with practical Python implementation.

Contribution

The paper proposes a novel dependency function that satisfies all desired properties for measuring dependence between variables, improving upon existing measures.

Findings

The new dependency function is theoretically sound and meets all proposed properties.

Python code implementation is provided for practical use.

The function offers a more general measure of dependence than traditional correlation.

Abstract

Measuring and quantifying dependencies between random variables (RV's) can give critical insights into a data-set. Typical questions are: `Do underlying relationships exist?', `Are some variables redundant?', and `Is some target variable $Y$ highly or weakly dependent on variable $X$?' Interestingly, despite the evident need for a general-purpose measure of dependency between RV's, common practice of data analysis is that most data analysts use the Pearson correlation coefficient (PCC) to quantify dependence between RV's, while it is well-recognized that the PCC is essentially a measure for linear dependency only. Although many attempts have been made to define more generic dependency measures, there is yet no consensus on a standard, general-purpose dependency function. In fact, several ideal properties of a dependency function have been proposed, but without much argumentation. Motivated by this, in this paper we will discuss and revise the list of desired properties and propose a new dependency function that meets all these requirements. This general-purpose dependency function provides data analysts a powerful means to quantify the level of dependence between variables. To this end, we also provide Python code to determine the dependency function for use in practice.