Fused Mean-variance Filter for Feature Screening

TL;DR

This paper introduces a new model-free feature screening method called the fused mean-variance filter, suitable for ultrahigh dimensional data with various variable types and robust to heavy tails and dependencies.

Contribution

It develops a novel fused mean-variance index for feature screening that is model-free, versatile for different variable types, and effective under heavy-tailed or dependent data.

Findings

The method achieves sure screening and rank consistency.

Simulation studies show superior performance over existing methods.

Real data analysis demonstrates practical applicability.

Abstract

This paper proposes a novel model-free screening procedure for ultrahigh dimensional data analysis. By utilizing slicing technique which has been successfully ap- plied to continuous variables, we construct a new index called the fused mean-variance for feature screening. This method has the following merits: (i) it is model-free, i.e., without specifying regression form of predictors and response variable; (ii) it can be used to analyze various types of variables including discrete, categorical and continuous vari- ables; (iii) it still works well even when the covariates/random errors are heavy-tailed or the predictors are strongly dependent. Under some regularity conditions, we establish the sure screening and rank consistency. Simulation studies are conducted to assess the performance of the proposed approach. A real data is used to illustrate the proposed method.