Comment by derbOac
4 years ago
Also worth looking at the cited and related paper with the same author:
https://arxiv.org/abs/1910.12327
This follow-up paper presents a related measure of conditional dependence that has a "natural interpretation as a nonlinear generalization of the familiar partial R2 statistic for measuring conditional dependence by regression."
The follow-up paper also provides some additional interpretive insights, I think.
My intuitive impression is that both of these are important developments.
I also have a very vague suspicion, based on the form of the function, that the correlation measure has some interpretation in terms of mutual information involving rank transformations of random variables.
Thanks for finding this article. I agree, these are important developments in particular because so many econometric models are now using machine learning without any distributional assumptions. Using correlation coefficients based on linearity is grossly insufficient.