Also worth looking at the cited and related paper with the same author: https://arxiv.org/abs/1910.12327 https://arxiv.org/abs/1910.12327 This follow-up paper

Also worth looking at the cited and related paper with the same author: https://arxiv.org/abs/1910.12327 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.