# AUC Maximization from Biased Positive-unlabeled Data with Confidence

arXiv: https://arxiv.org/abs/2609.10928 · HTML: https://mlsanity.com/paper/2609.10928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 65 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Human uncertainty makes classification more robust](https://mlsanity.com/paper/1908.07086/) (2019)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Large-scale Robust Deep AUC Maximization: A New Surrogate Loss and Empirical Studies on Medical Image Classification](https://mlsanity.com/paper/2012.03173/) (2020)
- [Benchmarking Distribution Shift in Tabular Data with TableShift](https://mlsanity.com/paper/2312.07577/) (2023)
- [Confidence Scores Make Instance-dependent Label-noise Learning Possible](https://mlsanity.com/paper/2001.03772/) (2020)
- [Stochastic AUC Maximization with Deep Neural Networks](https://mlsanity.com/paper/1908.10831/) (2019)
- [A Closer Look at AUROC and AUPRC under Class Imbalance](https://mlsanity.com/paper/2401.06091/) (2024)
- [On Symmetric Losses for Learning from Corrupted Labels](https://mlsanity.com/paper/1901.09314/) (2019)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [Is the Performance of My Deep Network Too Good to Be True? A Direct Approach to Estimating the Bayes Error in Binary Classification](https://mlsanity.com/paper/2202.00395/) (2022)
- [Binary Classification from Positive-Confidence Data](https://mlsanity.com/paper/1710.07138/) (2017)
- [Semi-Supervised AUC Optimization based on Positive-Unlabeled Learning](https://mlsanity.com/paper/1705.01708/) (2017)
- [Pointwise Binary Classification with Pairwise Confidence Comparisons](https://mlsanity.com/paper/2010.01875/) (2020)
- [Learning from Similarity-Confidence Data](https://mlsanity.com/paper/2102.06879/) (2021)
- [Instance-Dependent PU Learning by Bayesian Optimal Relabeling](https://mlsanity.com/paper/1808.02180/) (2018)
- [Learning from Multiple Expert Annotators for Enhancing Anomaly Detection in Medical Image Analysis](https://mlsanity.com/paper/2203.10611/) (2022)
- [Binary Classification with Confidence Difference](https://mlsanity.com/paper/2310.05632/) (2023)
- [Weakly Supervised AUC Optimization: A Unified Partial AUC Approach](https://mlsanity.com/paper/2305.14258/) (2023)
- [Binary Classification from Positive Data with Skewed Confidence](https://mlsanity.com/paper/2001.10642/) (2020)
- [Practical estimation of the optimal classification error with soft labels and calibration](https://mlsanity.com/paper/2505.20761/) (2025)
- [Interestingness First Classifiers](https://mlsanity.com/paper/2508.19780/) (2025)

## Abstract (arXiv)

Maximizing the area under the receiver operating characteristic curve (AUC) is a standard approach to imbalanced binary classification. Although positive and negative data are required for maximizing the AUC, negative data are often difficult to collect in some real-world applications due to privacy concerns or the need for specialized expertise to annotate them. Thus, AUC maximization from positive and unlabeled (PU) data has been attracting attention. Existing methods assume that labeled positive data are unbiased samples from the true positive distribution. However, this ideal assumption is often violated in practice. In this paper, we propose a method to maximize the AUC from biased PU data. To address the bias, our key idea is to exploit it confidence, i.e., the probability that an instance is positive, associated with the small number of labeled positive data. We derive an estimator of the AUC risk using biased PU data with confidence, enabling AUC maximization under such bias. We further show that the rewritten AUC risk induces a Bayes-optimal AUC ranking even when the available confidence is any strictly increasing transformation of the true posterior probability. We experimentally show the effectiveness of our method on eight real-world datasets.