# Semi-Supervised AUC Optimization based on Positive-Unlabeled Learning

## TL;DR

This paper introduces a semi-supervised AUC optimization method that effectively utilizes positive and unlabeled data without relying on strong distributional assumptions, improving performance in imbalanced classification tasks.

## Contribution

The paper proposes a novel PU-AUC method and extends it to semi-supervised learning, removing restrictive assumptions and proving unlabeled data's beneficial impact.

## Key findings

- Unlabeled data improves generalization in AUC optimization.
- The proposed methods outperform existing approaches in experiments.
- The approach is effective without strong distributional assumptions.

## Abstract

Maximizing the area under the receiver operating characteristic curve (AUC) is a standard approach to imbalanced classification. So far, various supervised AUC optimization methods have been developed and they are also extended to semi-supervised scenarios to cope with small sample problems. However, existing semi-supervised AUC optimization methods rely on strong distributional assumptions, which are rarely satisfied in real-world problems. In this paper, we propose a novel semi-supervised AUC optimization method that does not require such restrictive assumptions. We first develop an AUC optimization method based only on positive and unlabeled data (PU-AUC) and then extend it to semi-supervised learning by combining it with a supervised AUC optimization method. We theoretically prove that, without the restrictive distributional assumptions, unlabeled data contribute to improving the generalization performance in PU and semi-supervised AUC optimization methods. Finally, we demonstrate the practical usefulness of the proposed methods through experiments.