The Kolmogorov filter for variable screening in high-dimensional binary classification

Abstract

Variable screening techniques have been proposed to mitigate the impact of high dimensionality in classification problems, including t-test marginal screening (Fan & Fan, 2008) and maximum marginal likelihood screening (Fan & Song, 2010). However, these methods rely on strong modelling assumptions that are easily violated in real applications. To circumvent the parametric modelling assumptions, we propose a new variable screening technique for binary classification based on the Kolmogorov–Smirnov statistic. We prove that this so-called Kolmogorov filter enjoys the sure screening property under much weakened model assumptions. We supplement our theoretical study by a simulation study.