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

arXiv: https://arxiv.org/abs/2206.11655 · HTML: https://mlsanity.com/paper/2206.11655/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 88 references that are in the map.
- First posted on arXiv 23 Jun 2022.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Future Frame Prediction for Anomaly Detection -- A New Baseline](https://mlsanity.com/paper/1712.09867/) (2017)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [A Semi-supervised Graph Attentive Network for Financial Fraud Detection](https://mlsanity.com/paper/2003.01171/) (2020)
- [A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singleton](https://mlsanity.com/paper/2006.04045/) (2020)
- [Stochastic AUC Maximization with Deep Neural Networks](https://mlsanity.com/paper/1908.10831/) (2019)
- [Generalization bounds for deep convolutional neural networks](https://mlsanity.com/paper/1905.12600/) (2019)
- [One-Pass AUC Optimization](https://mlsanity.com/paper/1305.1363/) (2013)
- [Scalable Learning of Non-Decomposable Objectives](https://mlsanity.com/paper/1608.04802/) (2016)
- [Learning with Multiclass AUC: Theory and Algorithms](https://mlsanity.com/paper/2107.13171/) (2021)
- [Online and Stochastic Gradient Methods for Non-decomposable Loss Functions](https://mlsanity.com/paper/1410.6776/) (2014)
- [Federated Deep AUC Maximization for Heterogeneous Data with a Constant Communication Complexity](https://mlsanity.com/paper/2102.04635/) (2021)
- [Sparse-GAN: Sparsity-constrained Generative Adversarial Network for Anomaly Detection in Retinal OCT Image](https://mlsanity.com/paper/1911.12527/) (2019)
- [Support Vector Algorithms for Optimizing the Partial Area Under the ROC Curve](https://mlsanity.com/paper/1605.04337/) (2016)
- [Two-Way Partial AUC and Its Properties](https://mlsanity.com/paper/1508.00298/) (2015)
- [Local Rademacher Complexity Bounds based on Covering Numbers](https://mlsanity.com/paper/1510.01463/) (2015)
- [Top Rank Optimization in Linear Time](https://mlsanity.com/paper/1410.1462/) (2014)
- [Implicit Rate-Constrained Optimization of Non-decomposable Objectives](https://mlsanity.com/paper/2107.10960/) (2021)
- [Partial AUC optimization based deep speaker embeddings with class-center learning for text-independent speaker verification](https://mlsanity.com/paper/1911.08077/) (2019)
- [Mining Unfollow Behavior in Large-Scale Online Social Networks via Spatial-Temporal Interaction](https://mlsanity.com/paper/1911.07156/) (2019)
- [Speaker Verification By Partial AUC Optimization With Mahalanobis Distance Metric Learning](https://mlsanity.com/paper/1902.00889/) (2019)
- [Open-Narrow-Synechiae Anterior Chamber Angle Classification in AS-OCT Sequences](https://mlsanity.com/paper/2006.05367/) (2020)

## Built on by (most cited first, 15 of 15)

- [Frequency Perception Network for Camouflaged Object Detection](https://mlsanity.com/paper/2308.08924/) (2023)
- [Envisioning Outlier Exposure by Large Language Models for Out-of-Distribution Detection](https://mlsanity.com/paper/2406.00806/) (2024)
- [AUCSeg: AUC-oriented Pixel-level Long-tail Semantic Segmentation](https://mlsanity.com/paper/2409.20398/) (2024)
- [Size-invariance Matters: Rethinking Metrics and Losses for Imbalanced Multi-object Salient Object Detection](https://mlsanity.com/paper/2405.09782/) (2024)
- [OpenworldAUC: Towards Unified Evaluation and Optimization for Open-world Prompt Tuning](https://mlsanity.com/paper/2505.05180/) (2025)
- [Not All Pairs are Equal: Hierarchical Learning for Average-Precision-Oriented Video Retrieval](https://mlsanity.com/paper/2407.15566/) (2024)
- [MixBridge: Heterogeneous Image-to-Image Backdoor Attack through Mixture of Schr"odinger Bridges](https://mlsanity.com/paper/2505.08809/) (2025)
- [MoMa: Modulating Mamba for Adapting Image Foundation Models to Video Recognition](https://mlsanity.com/paper/2506.23283/) (2025)
- [Generalizable Prompt Learning of CLIP: A Brief Overview](https://mlsanity.com/paper/2503.01263/) (2025)
- [Enhancing Target-unspecific Tasks through a Features Matrix](https://mlsanity.com/paper/2505.03414/) (2025)
- [U-Trustworthy Models.Reliability, Competence, and Confidence in Decision-Making](https://mlsanity.com/paper/2401.02062/) (2024)
- [Stochastic Primal-Dual Double Block-Coordinate for Two-way Partial AUC Maximization](https://mlsanity.com/paper/2505.21944/) (2025)
- [Towards Size-invariant Salient Object Detection: A Generic Evaluation and Optimization Approach](https://mlsanity.com/paper/2509.15573/) (2025)
- [Closing the Approximation Gap of Partial AUC Optimization: A Tale of Two Formulations](https://mlsanity.com/paper/2512.01213/) (2025)
- [Enhancing Deep Neural Network Reliability with Refinement and Calibration](https://mlsanity.com/paper/2605.23249/) (2026)

## Abstract (arXiv)

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 mathsfTPR ≥ α, mathsfFPR ≤ β 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.