The Kendall Interaction Filter for Variable Interaction Screening in Ultra High Dimensional Classification Problems

Abstract

Accounting for important interaction effects can improve prediction of many statistical learning models. Identification of relevant interactions, however, is a challenging issue owing to their ultrahigh-dimensional nature. Interaction screening strategies can alleviate such issues. However, due to heavier tail distribution and complex dependence structure of interaction effects, innovative robust and/or model-free methods for screening interactions are required to better scale analysis of complex and high-throughput data. In this work, we develop a new model-free interaction screening method, termed Kendall Interaction Filter (KIF), for the classification in high-dimensional settings. The KIF method suggests a weighted-sum measure, which compares the overall to the within-cluster Kendall's $\tau$ of pairs of predictors, to select interactive couples of features. The proposed KIF measure captures relevant interactions for the clusters response-variable, handles continuous, categorical or a mixture of continuous-categorical features, and is invariant under monotonic transformations. We show that the KIF measure enjoys the sure screening property in the high-dimensional setting under mild conditions, without imposing sub-exponential moment assumptions on the features' distributions. We illustrate the favorable behavior of the proposed methodology compared to the methods in the same category using simulation studies, and we conduct real data analyses to demonstrate its utility.