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Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence by Huang, Zhen; Deb, Nabarun; Sen, Bodhisattva is a scholarly article available to read on EtoBox.

What is Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence about?

In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of conditional dependence between two random variables $Y$ and $Z$ given a third variable $X$, all taking values in general topological spaces. The population version of any of these measures captures the strength of conditional dependence and it is 0 if and only if $Y$ and $Z$ are conditionally independent given $X$, and 1 if and only if $Y$ is a measurable function of $Z$ and $X$. Thus, our measure -- which we call kernel partial correlation (KPC) coefficient -- can be thought of as a nonparametric generalization of the partial correlation coefficient that possesses the above properties when $(X,Y,Z)$ is jointly normal. We describe two consistent methods of estimating KPC. Our first method utilizes the general framework of geometric graphs, including $K$-nearest neighbor graphs and minimum spanning trees. A sub-class of these estimators can be computed in near linear time and converges at a rate that automatically adapts to the intrinsic dimension(s) of the underlying distribution(s). Our second strategy involves direct estimation of conditional mean embeddings using cross-covariance o

Author

Huang, Zhen; Deb, Nabarun; Sen, Bodhisattva

Published

2020

Language

EN