Model-Free Feature Screening Based on Gini Impurity for Ultrahigh-Dimensional Multiclass Classification

Abstract

It is quite common that both categorical and continuous covariates appear in the data. But, most feature screening methods for ultrahigh-dimensional classification assume the covariates are continuous. And applicable feature screening method is very limited; to handle this non-trivial situation, we propose a model-free feature screening for ultrahigh-dimensional multi-classification with both categorical and continuous covariates. The proposed feature screening method will be based on Gini impurity to evaluate the prediction power of covariates. Under certain regularity conditions, it is proved that the proposed screening procedure possesses the sure screening property and ranking consistency properties. We demonstrate the finite sample performance of the proposed procedure by simulation studies and illustrate using real data analysis.