Cost-Aware AUC Optimization via Adaptive Kernel Density Estimation.

Area of Science:

• Machine Learning
• Statistical Modeling
• Predictive Analytics

Background:

• Area Under the ROC Curve (AUC) is a standard metric for model performance evaluation.
• Existing AUC optimization methods often assume parametric threshold distributions, which may not reflect real-world non-parametric cost distributions.
• Optimal decision thresholds are influenced by misclassification costs, necessitating a cost-aware approach.

Purpose of the Study:

• Introduce Cost-aware AUC (CAUC) to account for non-parametric cost distributions.
• Address the bilevel optimization challenges inherent in CAUC.
• Develop a robust and theoretically sound optimization framework for CAUC.

Main Methods:

• Applied convex relaxation to transform the non-convex inner optimization problem into a convex one.
• Developed an adaptive kernel density estimation framework to handle the derivative of the False Positive Rate (FPR).
• Utilized a finite-difference-based stochastic algorithm for model optimization, avoiding manual aggregation function design.

Main Results:

• The proposed algorithm achieves a theoretical convergence rate of O(ε⁻⁴).
• Empirical studies demonstrate the effectiveness and soundness of the CAUC framework across various datasets.
• The methods successfully address the non-convexity and derivative estimation challenges in CAUC optimization.

Conclusions:

• The developed framework provides an effective solution for optimizing Cost-aware AUC.
• The approach is robust and adaptable to different datasets and cost distributions.
• This work advances model evaluation by incorporating non-parametric misclassification costs.