  (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.
