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Title: Quantifying directed dependence via dimension reduction Authors:  Sebastian Fuchs - University of Salzburg (Austria) [presenting]
Abstract: A bivariate copula is defined that captures the scale-invariant extent of dependence of a single random variable Y on a set of potential explanatory random variables $X_1,\ldots, X_d$. The copula itself contains the information on whether $Y$ is completely dependent on $X_1,\ldots, X_d$, and whether $Y$ and $X_1,\ldots, X_d$ are independent. Evaluating this copula uniformly along the diagonal, i.e., calculating Spearman's footrule, leads to the so-called `simple measure of conditional dependence'. On the other hand, evaluating this copula uniformly over the unit square, i.e., calculating Spearman's rho, leads to a distribution-free coefficient of determination. We demonstrate the broad applicability of the above methodology in the context of feature selection and variable selection.