Rethinking and Reweighting the Univariate Losses for Multi-Label Ranking: Consistency and Generalization

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 .