Variable Screening Methods in Multi-Category Problems for Ultra-High Dimensional Data

Abstract

Variable screening techniques are fast and crude techniques to scan high-dimensional data and conduct dimension reduction before a refined variable selection method is applied. Its marginal analysis feature makes the method computationally feasible for ultra-high dimensional problems. However, most existing screening methods for classification problems are designed only for binary classification problems. There is lack of a comprehensive study on variable screening for multi-class classification problems. This research aims to fill the gap by developing variable screening for multi-class problems, to meet the need of high dimensional classification. The work has useful applications in cancer study, medicine, engineering and biology. In this research, we propose and investigate new and effective screening methods for multi-class classification problems. We consider two types of screening methods. The first one conducts screening for multiple binary classification problems separately and then aggregates the selected variables. The second one conducts screening for multi-class classification problems directly. In particular, for each method we investigate important issues such as choices of classification algorithms, variable ranking, and model size determination. We implement various selection criteria and compare their performance. We conduct extensive simulation studies to evaluate and compare the proposed screening methods with existing ones, which show that the new methods are promising. Furthermore, we apply the proposed methods to four cancer studies. R code has been developed for each method.