A Robust-Equitable Copula Dependence Measure for Feature Selection

Feature selection aims to select relevant features to improve the performance of predictors. Many feature selection methods depend on the choice of dependence measures. To select features that have complex nonlinear relationships with the response variable, the dependence measure should be equitable; i.e., it should treat linear and nonlinear relationships equally. In this paper, we introduce the concept of robust-equitability and identify a robust-equitable dependence measure robust copula dependence (RCD). This measure has the following advantages compared to existing dependence measures: it is robust to different relationship forms and robust to unequal sample sizes of different features. In contrast, existing dependence measures cannot take these factors into account simultaneously. Experiments on synthetic and realworld datasets confirm our theoretical analysis, and illustrate its advantage in feature selection.