# Towards Understanding Generalization of Macro-AUC in Multi-label Learning

arXiv: https://arxiv.org/abs/2305.05248 · HTML: https://mlsanity.com/paper/2305.05248/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 11 of 11)

- [Asymmetric Loss For Multi-Label Classification](https://mlsanity.com/paper/2009.14119/) (2020)
- [Distribution-Balanced Loss for Multi-Label Classification in Long-Tailed Datasets](https://mlsanity.com/paper/2007.09654/) (2020)
- [A Unified View of Multi-Label Performance Measures](https://mlsanity.com/paper/1609.00288/) (2016)
- [Barzilai-Borwein Step Size for Stochastic Gradient Descent](https://mlsanity.com/paper/1605.04131/) (2016)
- [Convex Calibrated Surrogates for the Multi-Label F-Measure](https://mlsanity.com/paper/2009.07801/) (2020)
- [On the Bayes-optimality of F-measure maximizers](https://mlsanity.com/paper/1310.4849/) (2013)
- [McDiarmid-Type Inequalities for Graph-Dependent Variables and Stability Bounds](https://mlsanity.com/paper/1909.02330/) (2019)
- [Multi-label classification: do Hamming loss and subset accuracy really conflict with each other?](https://mlsanity.com/paper/2011.07805/) (2020)
- [Joint Ranking SVM and Binary Relevance with Robust Low-Rank Learning for Multi-Label Classification](https://mlsanity.com/paper/1911.01658/) (2019)
- [Rethinking and Reweighting the Univariate Losses for Multi-Label Ranking: Consistency and Generalization](https://mlsanity.com/paper/2105.05026/) (2021)
- [Generalization bounds for learning under graph-dependence: A survey](https://mlsanity.com/paper/2203.13534/) (2022)

## Built on by (most cited first, 4 of 4)

- [Multi-Label Learning with Stronger Consistency Guarantees](https://mlsanity.com/paper/2407.13746/) (2024)
- [Top-K Pairwise Ranking: Bridging the Gap Among Ranking-Based Measures for Multi-Label Classification](https://mlsanity.com/paper/2407.06709/) (2024)
- [Towards Macro-AUC oriented Imbalanced Multi-Label Continual Learning](https://mlsanity.com/paper/2412.18231/) (2024)
- [Principled Algorithms for Optimizing Generalized Metrics in Multi-Label Learning](https://mlsanity.com/paper/2605.28767/) (2026)

## Abstract (arXiv)

Macro-AUC is the arithmetic mean of the class-wise AUCs in multi-label learning and is commonly used in practice. However, its theoretical understanding is far lacking. Toward solving it, we characterize the generalization properties of various learning algorithms based on the corresponding surrogate losses w.r.t. Macro-AUC. We theoretically identify a critical factor of the dataset affecting the generalization bounds: the label-wise class imbalance. Our results on the imbalance-aware error bounds show that the widely-used univariate loss-based algorithm is more sensitive to the label-wise class imbalance than the proposed pairwise and reweighted loss-based ones, which probably implies its worse performance. Moreover, empirical results on various datasets corroborate our theory findings. To establish it, technically, we propose a new (and more general) McDiarmid-type concentration inequality, which may be of independent interest.