# Rethinking Consistent Multi-Label Classification Under Inexact Supervision

arXiv: https://arxiv.org/abs/2510.04091 · HTML: https://mlsanity.com/paper/2510.04091/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 59 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 27 of 27)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Dual T: Reducing Estimation Error for Transition Matrix in Label-noise Learning](https://mlsanity.com/paper/2006.07805/) (2020)
- [Learning a Deep ConvNet for Multi-label Classification with Partial Labels](https://mlsanity.com/paper/1902.09720/) (2019)
- [The Emerging Trends of Multi-Label Learning](https://mlsanity.com/paper/2011.11197/) (2020)
- [Learning with Biased Complementary Labels](https://mlsanity.com/paper/1711.09535/) (2017)
- [Multi-Label Learning from Single Positive Labels](https://mlsanity.com/paper/2106.09708/) (2021)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Learning Noise Transition Matrix from Only Noisy Labels via Total Variation Regularization](https://mlsanity.com/paper/2102.02414/) (2021)
- [Do We Need Zero Training Loss After Achieving Zero Training Error?](https://mlsanity.com/paper/2002.08709/) (2020)
- [Mixture Proportion Estimation and PU Learning: A Modern Approach](https://mlsanity.com/paper/2111.00980/) (2021)
- [Multi-Label Learning with Global and Local Label Correlation](https://mlsanity.com/paper/1704.01415/) (2017)
- [A Unified View of Multi-Label Performance Measures](https://mlsanity.com/paper/1609.00288/) (2016)
- [Mitigating Overfitting in Supervised Classification from Two Unlabeled Datasets: A Consistent Risk Correction Approach](https://mlsanity.com/paper/1910.08974/) (2019)
- [Class-Distribution-Aware Pseudo Labeling for Semi-Supervised Multi-Label Learning](https://mlsanity.com/paper/2305.02795/) (2023)
- [Rethinking Class-Prior Estimation for Positive-Unlabeled Learning](https://mlsanity.com/paper/2002.03673/) (2020)
- [Binary Classification with Confidence Difference](https://mlsanity.com/paper/2310.05632/) (2023)
- [Realistic Evaluation of Deep Partial-Label Learning Algorithms](https://mlsanity.com/paper/2502.10184/) (2025)
- [Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practical](https://mlsanity.com/paper/2311.15502/) (2023)
- [CCMN: A General Framework for Learning with Class-Conditional Multi-Label Noise](https://mlsanity.com/paper/2105.07338/) (2021)
- [Mixture Proportion Estimation Beyond Irreducibility](https://mlsanity.com/paper/2306.01253/) (2023)
- [AdaFlood: Adaptive Flood Regularization](https://mlsanity.com/paper/2311.02891/) (2023)
- [Complementary to Multiple Labels: A Correlation-Aware Correction Approach](https://mlsanity.com/paper/2302.12987/) (2023)

## Built on by (most cited first, 3 of 3)

- [Mind the Way You Select Negative Texts: Pursuing the Distance Consistency in OOD Detection with VLMs](https://mlsanity.com/paper/2603.02618/) (2026)
- [Learning from Label Proportions with Dual-proportion Constraints](https://mlsanity.com/paper/2603.21153/) (2026)
- [Recent advances in weakly supervised learning: New supervision paradigms, assumption relaxations, and practical solutions](https://mlsanity.com/paper/2608.06896/) (2026)

## Abstract (arXiv)

Partial multi-label learning and complementary multi-label learning are two popular weakly supervised multi-label classification paradigms that aim to alleviate the high annotation costs of collecting precisely annotated multi-label data. In partial multi-label learning, each instance is annotated with a candidate label set, among which only some labels are relevant; in complementary multi-label learning, each instance is annotated with complementary labels indicating the classes to which the instance does not belong. Existing consistent approaches for the two paradigms either require accurate estimation of the generation process of candidate or complementary labels or assume a uniform distribution to eliminate the estimation problem. However, both conditions are usually difficult to satisfy in real-world scenarios. In this paper, we propose consistent approaches that do not rely on the aforementioned conditions to handle both problems in a unified way. Specifically, we propose two risk estimators based on first- and second-order strategies. Theoretically, we prove consistency w.r.t. two widely used multi-label classification evaluation metrics and derive convergence rates for the estimation errors of the proposed risk estimators. Empirically, extensive experimental results on both real-world and synthetic datasets validate the effectiveness of our proposed approaches against state-of-the-art methods.