Optimizing Two-way Partial AUC with an End-to-end Framework

TL;DR

This paper introduces a novel end-to-end framework for optimizing the Two-way Partial AUC (TPAUC), a metric focusing on high TPR and low FPR regions, with theoretical guarantees and empirical validation.

Contribution

It presents the first method to optimize TPAUC directly using surrogate loss functions, enabling efficient deep learning training with theoretical performance bounds.

Findings

Framework achieves superior TPAUC performance on benchmarks.

The surrogate optimization bounds the original TPAUC objective.

The method demonstrates strong generalization in experiments.

Abstract

The Area Under the ROC Curve (AUC) is a crucial metric for machine learning, which evaluates the average performance over all possible True Positive Rates (TPRs) and False Positive Rates (FPRs). Based on the knowledge that a skillful classifier should simultaneously embrace a high TPR and a low FPR, we turn to study a more general variant called Two-way Partial AUC (TPAUC), where only the region with $\mathsf{TPR} \ge \alpha, \mathsf{FPR} \le \beta$ is included in the area. Moreover, recent work shows that the TPAUC is essentially inconsistent with the existing Partial AUC metrics where only the FPR range is restricted, opening a new problem to seek solutions to leverage high TPAUC. Motivated by this, we present the first trial in this paper to optimize this new metric. The critical challenge along this course lies in the difficulty of performing gradient-based optimization with end-to-end stochastic training, even with a proper choice of surrogate loss. To address this issue, we propose a generic framework to construct surrogate optimization problems, which supports efficient end-to-end training with deep learning. Moreover, our theoretical analyses show that: 1) the objective function of the surrogate problems will achieve an upper bound of the original problem under mild conditions, and 2) optimizing the surrogate problems leads to good generalization performance in terms of TPAUC with a high probability. Finally, empirical studies over several benchmark datasets speak to the efficacy of our framework.