B1644
Title: A simple extension of Azadkia \& Chatterjee's rank correlation to a vector of endogenous variables
Authors: Jonathan Ansari - University of Salzburg (Austria) [presenting]
Sebastian Fuchs - University of Salzburg (Austria)
Abstract: As a direct extension of Azadkia \& Chatterjee's rank correlation $T$ to a set of $q$ output variables, the novel measure $T_q$, introduced and investigated recently, quantifies the scale-invariant extent of functional dependence of an output vector $Y = (Y1,..., Yq)$ on a number of $p$ input variables $X = (X_1,\ldots, X_p)$ and fulfils all the desired characteristics of a measure of predictability, namely $0 \le T_q(Y|X)\le 1$, $T_q(Y|X) = 0$ if and only if $Y$ and $X$ are independent, and $T_q(Y|X) = 1$ if and only if $Y$ is perfectly dependent on $X$. Based on various useful properties of $T_q(Y|X)$, a model-free and dependence-based feature ranking and forward feature selection of data with multiple response variables is presented, thus facilitating the selection of the most relevant explanatory variables.
