Comparing Two Categorical Gini Correlations with Applications to Classification Problems

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Assessing predictor importance is crucial in classification tasks.
• Existing methods may have limitations with categorical outcomes and complex predictor structures.
• The categorical Gini correlation (CGC) offers a measure of dependence between numerical predictors and categorical outcomes.

Purpose of the Study:

• To propose an inferential framework for comparing predictor importance in classification problems with categorical response variables.
• To extend the application of the categorical Gini correlation (CGC) for hypothesis testing on predictor importance.
• To provide a robust methodology that handles predictors of arbitrary dimensions and dependencies.

Main Methods:

• The framework utilizes the categorical Gini correlation (CGC) to quantify predictor-outcome association.
• Predictor importance is assessed by testing differences in CGCs between predictor groups.
• Asymptotic normality of the test statistic is derived, and a nonparametric bootstrap procedure is developed for inference.

Main Results:

• The proposed inferential framework effectively compares predictor importance for categorical outcomes.
• The methodology accommodates predictors with arbitrary and unequal dimensions, and inter-predictor dependencies.
• Theoretical properties including asymptotic normality and consistency are established for the test statistic.

Conclusions:

• The developed framework provides a statistically sound method for evaluating predictor importance in classification with categorical variables.
• The approach is validated through simulation studies and practical applications in breast cancer and human activity recognition.
• This work offers a valuable tool for researchers and practitioners in machine learning and data analysis.