The (partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical efforts on multi-label ranking mainly focus on (Fisher) consistency analyses. However, there is a gap between existing theory and practice --- some inconsistent pairwise losses can lead to promising performance, while some consistent univariate losses usually have no clear superiority in practice. To take a step towards filling up this gap, this paper presents a systematic study from two complementary perspectives of consistency and generalization error bounds of learning algorithms. We theoretically find two key factors of the distribution (or dataset) that affect the learning guarantees of algorithms: the instance-wise class imbalance and the label size $c$. Specifically, in an extremely imbalanced case, the algorithm with the consistent univariate loss has an error bound of $O(c)$, while the one with the inconsistent pairwise loss depends on $O(\sqrt{c})$ as shown in prior work. This may shed light on the superior performance of pairwise methods in practice, where real datasets are usually highly imbalanced. Moreover, we present an inconsistent reweighted univariate loss-based algorithm that enjoys an error bound of $O(\sqrt{c})$ for promising performance as well as the computational efficiency of univariate losses. Finally, experimental results confirm our theoretical findings.

The (partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical efforts on multi-label ranking mainly focus on (Fisher) consistency analyses. However, there is a gap between existing theory and practice --- some inconsistent pairwise losses can lead to promising performance, while some consistent univariate losses usually have no clear superiority in practice. To take a step towards filling up this gap, this paper presents a systematic study from two complementary perspectives of consistency and generalization error bounds of learning algorithms. We theoretically find two key factors of the distribution (or dataset) that affect the learning guarantees of algorithms: the instance-wise class imbalance and the label size c .

(Partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical work on multi-label ranking mainly focuses on (Fisher) consistency analyses. However, there is a gap between existing theory and practice -- some pairwise losses can lead to promising performance but lack consistency, while some univariate losses are consistent but usually have no clear superiority in practice. In this paper, we attempt to fill this gap through a systematic study from two complementary perspectives of consistency and generalization error bounds of learning algorithms. Our results show that learning algorithms with the consistent univariate loss have an error bound of $O(c)$ ($c$ is the number of labels), while algorithms with the inconsistent pairwise loss depend on $O(\sqrt{c})$ as shown in prior work. This explains that the latter can achieve better performance than the former in practice. Moreover, we present an inconsistent reweighted univariate loss-based learning algorithm that enjoys an error bound of $O(\sqrt{c})$ for promising performance as well as the computational efficiency of univariate losses. Finally, experimental results validate our theoretical analyses.