The Area Under the ROC Curve (AUC) is a well-known metric for evaluating instance-level long-tail learning problems. In the past two decades, many AUC optimization methods have been proposed to improve model performance under long-tail distributions. In this paper, we explore AUC optimization methods in the context of pixel-level long-tail semantic segmentation, a much more complicated scenario. This task introduces two major challenges for AUC optimization techniques. On one hand, AUC optimization in a pixel-level task involves complex coupling across loss terms, with structured inner-image and pairwise inter-image dependencies, complicating theoretical analysis. On the other hand, we find that mini-batch estimation of AUC loss in this case requires a larger batch size, resulting in an unaffordable space complexity.

The Area Under the ROC Curve (AUC) is a well-known metric for evaluating instance-level long-tail learning problems. In the past two decades, many AUC optimization methods have been proposed to improve model performance under long-tail distributions. In this paper, we explore AUC optimization methods in the context of pixel-level long-tail semantic segmentation, a much more complicated scenario. This task introduces two major challenges for AUC optimization techniques. On one hand, AUC optimization in a pixel-level task involves complex coupling across loss terms, with structured inner-image and pairwise inter-image dependencies, complicating theoretical analysis. On the other hand, we find that mini-batch estimation of AUC loss in this case requires a larger batch size, resulting in an unaffordable space complexity.

Semi-supervised learning, which aims to construct learners that automatically exploit the large amount of unlabeled data in addition to the limited labeled data, has been widely applied in many real-world applications. AUC is a well-known performance measure for a learner, and directly optimizing AUC may result in a better prediction performance. Thus, semi-supervised AUC optimization has drawn much attention. Existing semi-supervised AUC optimization methods exploit unlabeled data by explicitly or implicitly estimating the possible labels of the unlabeled data based on various distributional assumptions. However, these assumptions may be violated in many real-world applications, and estimating labels based on the violated assumption may lead to poor performance. In this paper, we argue that, in semi-supervised AUC optimization, it is unnecessary to guess the possible labels of the unlabeled data or prior probability based on any distributional assumptions. We analytically show that the AUC risk can be estimated unbiasedly by simply treating the unlabeled data as both positive and negative. Based on this finding, two semi-supervised AUC optimization methods named Samult and Sampura are proposed. Experimental results indicate that the proposed methods outperform the existing methods.

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.