Independence testing and variable selection problems: non-Euclidean perspective

Abstract

Here we address the challenges associated with independence testing in non-Euclidean spaces, which are increasingly common in modern applications. Traditional approaches based on Euclidean distance measures often prove inadequate for data with spherical, hyperspherical, or other non-Euclidean structures, necessitating the development of new methodologies. We consider kernel-based generalizations of distance covariance that enable efficient independence testing in such spaces. Moreover, we explore its potential in marginal screening particularly when data components are of different types. Through extensive empirical studies, we demonstrate that our proposed approaches significantly enhance performance and accuracy in comparison to conventional methods.