Support Vector Algorithms for Optimizing the Partial Area under the ROC Curve.

Area of Science:

• Machine Learning
• Computational Statistics
• Pattern Recognition

Background:

• The Area Under the ROC Curve (AUC) is a standard machine learning metric.
• Partial AUC (pAUC) is increasingly used for specific performance ranges in applications like medicine and biometrics.
• Optimizing pAUC directly presents challenges due to its non-decomposable structure.

Purpose of the Study:

• To develop support vector algorithms for directly optimizing partial AUC between specified false-positive rates.
• To address the challenges in designing and optimizing convex surrogates for pAUC.
• To provide efficient algorithms for pAUC optimization in machine learning.

Main Methods:

• Utilized the structural Support Vector Machine (SVM) framework.
• Developed convex surrogates for pAUC by minimizing a suitable proxy objective.
• Employed a cutting plane solver, incorporating a novel polynomial-time algorithm for combinatorial optimization specific to pAUC.
• Applied difference-of-convex programming for optimizing a tighter non-convex hinge loss surrogate.

Main Results:

• Successfully designed and optimized convex surrogates for partial AUC.
• Developed an efficient polynomial-time algorithm for the combinatorial optimization subproblem in pAUC optimization.
• Demonstrated the efficacy of the proposed methods on real-world and benchmark datasets.
• Showcased an approach for optimizing a tighter non-convex surrogate for improved performance.

Conclusions:

• The developed support vector algorithms effectively optimize partial AUC directly.
• The novel combinatorial optimization algorithm significantly advances pAUC optimization efficiency.
• The methods offer a robust solution for performance evaluation in applications requiring specific operating ranges.
• The research provides valuable tools for machine learning practitioners in fields utilizing pAUC.