RECORD
Rethinking and Reweighting the Univariate Losses for Multi-Label Ranking: Consistency and Generalization
Machine Learning · Submitted 10 May 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
(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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | (Partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. | background 1.00 | 0.04 | 0.02 | asserted 0.99 |
| s1 | Prior theoretical work on multi-label ranking mainly focuses on (Fisher) consistency analyses. | background 1.00 | 0.03 | 0.02 | asserted 1.00 |
| s2 | 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. | gap 1.00 | 0.09 | 0.05 | asserted 0.77 |
| s3 | 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. | contribution 0.98 | 0.51 | 0.06 | asserted 0.50 |
| s4 | 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. | result 1.00 | 0.86 | 0.36 | asserted 1.00 |
| s5 | This explains that the latter can achieve better performance than the former in practice. | interpretation 1.00 | 0.39 | 0.23 | asserted 0.96 |
| s6 | 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. | contribution 0.63 | 0.95 | 0.31 | asserted 1.00 |
| s7 | Finally, experimental results validate our theoretical analyses. | result 0.88 | 0.89 | 0.09 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
(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.
Human review
How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
-
A widely used strategy for tackling this difficulty is to substitute the original loss function which is discontinuous with a continuous surrogate, which has been applied in many areas including ordinary classification [ref] , multi-label classification [ref] , AUC optimization [ref] , cost-sensitive learning [ref] , top-$K$ classification [ref] , adversarially robust classification [ref] , and learning to reject [ref] .
In Defense of Softmax Parametrization for Calibrated and Consistent Learning to Defer · Consistent Surrogate Losses for L2D · 0.93
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.