Generalized Gini dependence measures for complex data and their applications in K-sample problem and feature screening

Dependence between various objects is an important issue which has attracted many researchers. This paper will focus on a new Gini dependence measure having been proposed recently, which measures association between a continuous random vector and a categorical variable. We extend the original Gini method from three perspectives: to various RKHS, to various distance methods and to multi-factor variable. As numerical simulations revealed, Laplacian kernel Gini correlation is statistically efficient both for K-sample tests and for ultrahigh dimensional grouped feature screening. Moreover, we make robustness analysis and discuss the situations appropriate for different distance based Gini measures, including high dimensional sparse data, data with outliers, etc. Real data application implies the estimation accuracy of the proposed Laplacian kernel Gini correlation and its effectiveness for high dimensional K-sample tests. Grouped factor selection reduces time complexity with accuracy of regression models roughly maintained. Our Gini dependence for multi-factor data makes it possible for researchers to comprehensively analyze the impacts of attributes on multiple categorical outcomes.