Variable Importance Assessments and Backward Variable Selection for High-Dimensional Data

TL;DR

This paper introduces a novel distance-based variable importance measure and a backward selection algorithm for high-dimensional data, improving variable selection accuracy in genomic analysis and similar fields.

Contribution

It proposes a new variable importance assessment inspired by MRPP and a backward selection method tailored for high-dimensional variable selection.

Findings

Effective in identifying important variables in high-dimensional data

Outperforms existing methods in simulations and real data

Demonstrates good properties and advantages over other approaches

Abstract

Variable selection in high-dimensional scenarios is of great interested in statistics. One application involves identifying differentially expressed genes in genomic analysis. Existing methods for addressing this problem have some limits or disadvantages. In this paper, we propose distance based variable importance measures to deal with these problems, which is inspired by the Multi-Response Permutation Procedure (MRPP). The proposed variable importance assessments can effectively measure the importance of an individual dimension by quantifying its influence on the differences between multivariate distributions. A backward selection algorithm is developed that can be used in high-dimensional variable selection to discover important variables. Both simulations and real data applications demonstrate that our proposed method enjoys good properties and has advantages over other methods.