Significance analysis for pairwise variable selection in classification

The goal of this article is to select important variables that can distinguish one class of data from another. A marginal variable selection method ranks the marginal effects for classi cation of individual variables, and is a useful and efficient approach for variable selection. Our focus here is to consider the bivariate effect, in addition to the marginal effect. In particular, we are interested in those pairs of variables that can lead to accurate classi cation predictions when they are viewed jointly. To accomplish this, we propose a permutation test called Signi cance test of Joint Effect (SigJEff). In the absence of joint effect in the data, SigJEff is similar or equivalent to many marginal methods. However, when joint effects exist, our method can signi cantly boost the performance of variable selection. Such joint effects can help to provide additional, and sometimes dominating, advantage for classi cation. We illustrate and validate our approach using both simulated example and a real glioblastoma multiforme data set, which provide promising results