Comparing Two Categorical Gini Correlations with Applications to Classification Problems

TL;DR

This paper introduces a statistical framework for comparing predictor importance in classification tasks using categorical Gini correlation, with applications demonstrated on real datasets.

Contribution

It develops a novel inferential method for comparing CGCs across predictors, accommodating arbitrary predictor dimensions and dependence structures.

Findings

The test statistic is asymptotically normal under null and alternative hypotheses.

The bootstrap procedure provides a reliable inference alternative.

Applications show the method's effectiveness in real classification problems.

Abstract

This article proposes an inferential framework for comparing predictor importance in classification problems with categorical response variables. The approach is based on the categorical Gini correlation (CGC) proposed by Dang et al. (2020), a measure of dependence between numerical predictors and categorical outcomes. Predictor importance is evaluated by testing differences in CGCs across competing predictor groups. The proposed methodology accommodates predictors of arbitrary and unequal dimensions and allows for dependence between predictor groups. Asymptotic normality of the test statistic is established under both the null and alternative hypotheses, and the resulting test is shown to be consistent. In addition to deriving the asymptotic distribution, a nonparametric bootstrap procedure is developed as an alternative approach to inference. Simulation studies, along with applications to breast cancer and human activity recognition datasets, demonstrate the effectiveness of the proposed framework.