The mRMR variable selection method: a comparative study for functional data

TL;DR

This paper compares the traditional mRMR variable selection method with a modified version using distance correlation for functional data, demonstrating the new approach's superior performance through extensive simulations and real-data applications.

Contribution

It introduces a modified mRMR method replacing mutual information with distance correlation for better variable selection in functional data analysis.

Findings

The new mRMR method outperforms the original in simulations.

Extensive experiments validate the effectiveness of the modified approach.

Real-data examples confirm practical advantages of the new method.

Abstract

The use of variable selection methods is particularly appealing in statistical problems with functional data. The obvious general criterion for variable selection is to choose the `most representative' or `most relevant' variables. However, it is also clear that a purely relevance-oriented criterion could lead to select many redundant variables. The mRMR (minimum Redundance Maximum Relevance) procedure, proposed by Ding and Peng (2005) and Peng et al. (2005) is an algorithm to systematically perform variable selection, achieving a reasonable trade-off between relevance and redundancy. In its original form, this procedure is based on the use of the so-called mutual information criterion to assess relevance and redundancy. Keeping the focus on functional data problems, we propose here a modified version of the mRMR method, obtained by replacing the mutual information by the new association measure (called distance correlation) suggested by Sz\'ekely et al. (2007). We have also performed an extensive simulation study, including 1600 functional experiments (100 functional models $\times$ 4 sample sizes $\times$ 4 classifiers) and three real-data examples aimed at comparing the different versions of the mRMR methodology. The results are quite conclusive in favor of the new proposed alternative.