Multi-label ranking, which returns multiple top-ranked labels for each instance, has a wide range of applications for visual tasks. Due to its complicated setting, prior arts have proposed various measures to evaluate model performances. However, both theoretical analysis and empirical observations show that a model might perform inconsistently on different measures. To bridge this gap, this paper proposes a novel measure named Top-K Pairwise Ranking (TKPR), and a series of analyses show that TKPR is compatible with existing ranking-based measures. In light of this, we further establish an empirical surrogate risk minimization framework for TKPR. On one hand, the proposed framework enjoys convex surrogate losses with the theoretical support of Fisher consistency. On the other hand, we establish a sharp generalization bound for the proposed framework based on a novel technique named data-dependent contraction. Finally, empirical results on benchmark datasets validate the effectiveness of the proposed framework.

翻译：多标签排序任务为每个实例返回多个排名靠前的标签，在视觉任务中具有广泛的应用。由于其复杂的设定，先前研究提出了多种度量指标来评估模型性能。然而，理论分析和实证观察均表明，模型在不同度量指标上的表现可能存在不一致性。为弥合这一差距，本文提出了一种名为Top-K成对排序（TKPR）的新型度量指标，并通过系列分析证明TKPR与现有基于排序的度量指标具有兼容性。基于此，我们进一步建立了TKPR的经验代理风险最小化框架。该框架一方面具备凸代理损失函数，并得到Fisher一致性的理论支撑；另一方面，我们基于名为数据依赖收缩的新技术，为该框架建立了尖锐的泛化界。最终，在基准数据集上的实证结果验证了所提出框架的有效性。