The Area under the ROC curve (AUC) is a well-known ranking metric for problems such as imbalanced learning and recommender systems. The vast majority of existing AUC-optimization-based machine learning methods only focus on binary-class cases, while leaving the multiclass cases unconsidered. In this paper, we start an early trial to consider the problem of learning multiclass scoring functions via optimizing multiclass AUC metrics. Our foundation is based on the M metric, which is a well-known multiclass extension of AUC. We first pay a revisit to this metric, showing that it could eliminate the imbalance issue from the minority class pairs. Motivated by this, we propose an empirical surrogate risk minimization framework to approximately optimize the M metric. Theoretically, we show that: (i) optimizing most of the popular differentiable surrogate losses suffices to reach the Bayes optimal scoring function asymptotically; (ii) the training framework enjoys an imbalance-aware generalization error bound, which pays more attention to the bottleneck samples of minority classes compared with the traditional $O(\sqrt{1/N})$ result. Practically, to deal with the low scalability of the computational operations, we propose acceleration methods for three popular surrogate loss functions, including the exponential loss, squared loss, and hinge loss, to speed up loss and gradient evaluations. Finally, experimental results on 11 real-world datasets demonstrate the effectiveness of our proposed framework.

翻译：ROC 曲线( AUC ) 下的区域是众所周知的衡量不平衡学习和推荐系统等问题的标准。 绝大多数现有的ACU- 优化型机器学习方法仅侧重于二进制类案例, 而没有考虑多级案例。 在本文中, 我们开始早期试验, 以研究通过优化多级ACU衡量标准学习多级评分功能的问题。 我们的基础以M 衡量标准为基础, 这是AUC 众所周知的多级扩展。 我们首先对这个衡量标准进行重新审视, 表明它能够消除少数类伴侣之间的不平衡问题。 受此驱动, 我们提出了一个实验替代风险最小化框架, 以大致优化M 标准。 从理论上讲, 我们表明:(一) 优化大多数流行的可分级评分损失功能, 足以以最优的方式达到巴伊斯最佳评分功能。 (二) 培训框架有一个不平衡和普遍化的扩展错误, 与传统的 $O/ srlortialalalal dal develop commissional resultial develop le) ex real develop resultial develop exfulation exfulational dal dal developtions.