Stochastic Primal-Dual Double Block-Coordinate for Two-way Partial AUC Maximization

TL;DR

This paper introduces novel stochastic primal-dual double block-coordinate algorithms for optimizing two-way partial AUC in imbalanced binary classification, demonstrating faster convergence and improved performance over existing methods.

Contribution

The paper proposes the first stochastic primal-dual double block-coordinate algorithms for TPAUC maximization, applicable to both convex and non-convex problems, with theoretical convergence guarantees.

Findings

Algorithms achieve faster convergence on benchmark datasets.

Demonstrated superior generalization performance.

Theoretical analysis confirms improved convergence rates.

Abstract

Two-way partial AUC (TPAUC) is a critical performance metric for binary classification with imbalanced data, as it focuses on specific ranges of the true positive rate (TPR) and false positive rate (FPR). However, stochastic algorithms for TPAUC optimization remain under-explored, with existing methods either limited to approximated TPAUC loss functions or burdened by sub-optimal complexities. To overcome these limitations, we introduce two innovative stochastic primal-dual double block-coordinate algorithms for TPAUC maximization. These algorithms utilize stochastic block-coordinate updates for both the primal and dual variables, catering to both convex and non-convex settings. We provide theoretical convergence rate analyses, demonstrating significant improvements over prior approaches. Our experimental results, based on multiple benchmark datasets, validate the superior performance of our algorithms, showcasing faster convergence and better generalization. This work advances the state of the art in TPAUC optimization and offers practical tools for real-world machine learning applications.