An Interpretable Measure for Quantifying Predictive Dependence between Continuous Random Variables -- Extended Version
This addresses the need for interpretable dependence measures in statistical learning, offering a tool for researchers and practitioners, though it appears incremental as it builds on existing concepts with new interpretability features.
The authors tackled the problem of quantifying predictive dependence between continuous random variables by introducing a novel non-parametric measure that assesses association, including non-functional relationships, with interpretability based on expected relative loss in predictive accuracy. They evaluated it on over 90,000 datasets, showing it provides valuable insights where existing methods fail.
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.