An Interpretable Measure for Quantifying Predictive Dependence between Continuous Random Variables -- Extended Version

TL;DR

This paper introduces a new non-parametric, interpretable measure for quantifying dependence between continuous variables, capturing complex relationships and outperforming existing methods in diverse datasets.

Contribution

The paper presents a novel, fully non-parametric dependence measure that is interpretable, bounded, and capable of detecting a wide range of relationships, including non-functional ones.

Findings

The measure accurately detects independence and dependence in various datasets.

It outperforms existing dependence measures in benchmark tests.

The measure provides meaningful insights into complex variable relationships.

Abstract

A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between continuous variables $X$ and $Y$, capable of capturing a wide range of relationships, including non-functional ones. A key advantage of this measure is its interpretability: it quantifies the expected relative loss in predictive accuracy when the distribution of $X$ is ignored in predicting $Y$. This measure is bounded within the interval [0,1] and is equal to zero if and only if $X$ and $Y$ are independent. We evaluate the performance of our measure on over 90,000 real and synthetic datasets, benchmarking it against leading alternatives. Our results demonstrate that the proposed measure provides valuable insights into underlying relationships, particularly in cases where existing methods fail to capture important dependencies.