Model-Free Feature Screening via Maximal Information Coefficient (MIC) for Ultrahigh-Dimensional Multiclass Classification

Abstract

It is common for datasets to contain both categorical and continuous variables. However, many feature screening methods designed for high-dimensional classification assume that the variables are continuous. This limits the applicabil ity of existing methods in handling this complex scenario. To address this i ssue, we propose a model-free feature screening approach for ultra-high-dimensional multi-classification that can handle both categorical and continuous variables. Our proposed feature screening method utilizes the Maximal Information Coefficient to assess the predictive power of the variables. By satisfying certain regularity conditions, we have proven that our screening procedure possesses the sure screening property and ranking consistency properties. To validate the effectiveness of our approach, we conduct simulation studies and provide real data analysis examples to demonstrate its performance in finite samples. In summary, our proposed method offers a solution for effectively screening features in ultra-high-dimensional datasets with a mixture of categorical and continuous covariates.