Model-free feature screening for ultrahigh-dimensional classification data

In this paper, we propose a robust semi-distance correlation (RSDCor for short) to measure the dependence between a categorical random variable Y∈ mathbbR¹ and a continuous random vector bm z∈ mathbbR^d (dgeq 1). RSDCor can be regarded as a generalization of semi-distance correlation (for short SDCor) proposed by Zhong et al. (2024). Compared with the SDCor, the significant advantage of the RSDCor is that it is relatively robust to heavy-tailed distributions or outliers. In addition, RSDCor satisfies 0≤mathrmRSDCorbm zY)≤ 1 and mathrmRSDCorbm zY)=0 if and only if bm zis independent of Y. Furthermore, we propose a feature screening procedure for ultrahigh-dimensional classification data based on RSDCor, which is abbreviated as RSD-SIS. In theory, we establish the sure screening 性质 and ranking consistency of the RSD-SIS. RSD-SIS enjoys several appealing merits. First, it does not require specific model assumptions or finite moment assumptions of predictor variables; second, it can also be directly used to screen grouped predictor variables and a categorical response variable; third, it allows the categorical response variable to have a diverging number of classes at a rate of O(n^κ) with some κgeq 0. Monte Carlo simulation and a real data analysis both indicate that RSD-SIS performs very well compared with the existing screening procedures.