Kernel‐based measures of association

Abstract

Measures of association have been widely used for describing statistical relationships between two sets of variables. Traditionally, such association measures focus on specialized settings. Based on an in-depth summary of existing common measures, we present a general framework for association measures that unifies existing methods and novel extensions based on kernels, including practical solutions to computational challenges. Specifically, we introduce association screening and variable selection via maximizing kernel-based association measures. We also develop a backward dropping procedure for feature selection when there are a large number of candidate variables. The proposed framework was evaluated by independence tests and feature selection using kernel association measures on a diversified set of simulated association patterns with different dimensions and variable types. The results show the superiority of the generalized association measures over existing ones. We also apply our framework to a real-world problem of gender prediction from handwritten texts. We demonstrate, through this application, the data-driven adaptation of kernels, and how kernel-based association measures can naturally be applied to data structures including functional input spaces. This suggests that the proposed framework can guide derivation of appropriate association measures in a wide range of real-world problems and work well in practice.

Dependence and dependence structures: estimation and visualization using the unifying concept of distance multivariance

“…There have been many methods employed and proposed, see e.g. [24], [43] and [29] for recent surveys. Usually these focus on the (functional) dependence of pairs of variables.…”