# A Robust AUC Maximization Framework with Simultaneous Outlier Detection and Feature Selection for Positive-Unlabeled Classification

**Authors:** Ke Ren, Haichuan Yang, Yu Zhao, Mingshan Xue, Hongyu Miao, Shuai Huang, Ji Liu  
**arXiv:** [1803.06604](https://arxiv.org/abs/1803.06604)  
**Date:** 2018-03-18  
**Summary page:** https://www.summarizepaper.com/en/paper/1803.06604v1/

## Key points

- Positive-Unlabeled (PU) classification is common in real-world applications like healthcare, text classification, and bioinformatics
- In PU classification, there are few labeled positive samples and a large volume of unlabeled samples that may contain both positive and negative samples
- The authors propose a robust learning framework for the PU problem that combines AUC maximization, outlier detection, and feature selection
- AUC maximization helps handle imbalanced data effectively
- Outlier detection improves the accuracy of the model by excluding wrong labels from training
- Feature selection aims to identify and exclude corrupted features that negatively impact classification performance
- The proposed model provides generalization error bounds and practical guidance for training
- Empirical comparisons on surgical site infection (SSI) and EEG seizure detection show that the proposed model outperforms existing methods
- This research presents a comprehensive framework for addressing the challenges of PU classification in healthcare and bioinformatics.

## Summary

The Positive-Unlabeled (PU) classification is a common scenario in real-world applications such as healthcare, text classification, and bioinformatics. In this scenario, we only have access to a few samples labeled as "positive" along with a large volume of "unlabeled" samples that may contain both positive and negative samples. Building a robust classifier for the PU problem is challenging, particularly when dealing with complex data where negative samples overwhelm and mislabeled samples or corrupted features exist. To address these challenges, the authors propose a robust learning framework that combines three key components: AUC maximization, outlier detection, and feature selection. AUC maximization is used as a robust metric for biased labels, allowing the classifier to handle imbalanced data effectively. Outlier detection helps exclude wrong labels from the training process, improving the overall accuracy of the model. Feature selection aims to identify and exclude corrupted features that may negatively impact classification performance. The proposed model provides generalization error bounds that offer valuable insight into its theoretical performance. These bounds also provide practical guidance for training the model; it is found that including unlabeled samples in the training process is sufficient as long as their sample size is comparable to the number of positive samples. To demonstrate the effectiveness of their approach, empirical comparisons are conducted on two real-world applications: surgical site infection (SSI) and EEG seizure detection. The results show that the proposed model outperforms existing methods in these applications. Overall, this research presents a comprehensive framework for addressing the challenges of PU classification by combining AUC maximization, outlier detection, and feature selection. The theoretical analysis provides insights into its performance characteristics while empirical evaluations on real-world datasets validate its effectiveness in practical applications such as healthcare and bioinformatics.