# CCMN: A General Framework for Learning with Class-Conditional Multi-Label Noise

arXiv: https://arxiv.org/abs/2105.07338 · HTML: https://mlsanity.com/paper/2105.07338/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 65 references that are in the map.
- First posted on arXiv 16 May 2021.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Multi-Label Image Recognition with Graph Convolutional Networks](https://mlsanity.com/paper/1904.03582/) (2019)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Learning from Noisy Labels with Distillation](https://mlsanity.com/paper/1703.02391/) (2017)
- [The Emerging Trends of Multi-Label Learning](https://mlsanity.com/paper/2011.11197/) (2020)
- [Masking: A New Perspective of Noisy Supervision](https://mlsanity.com/paper/1805.08193/) (2018)
- [Curriculum Loss: Robust Learning and Generalization against Label Corruption](https://mlsanity.com/paper/1905.10045/) (2019)
- [Toward Robustness against Label Noise in Training Deep Discriminative Neural Networks](https://mlsanity.com/paper/1706.00038/) (2017)
- [Classification with Asymmetric Label Noise: Consistency and Maximal Denoising](https://mlsanity.com/paper/1303.1208/) (2013)
- [Large-scale Multi-label Learning with Missing Labels](https://mlsanity.com/paper/1307.5101/) (2013)
- [Recurrent Attentional Reinforcement Learning for Multi-label Image Recognition](https://mlsanity.com/paper/1712.07465/) (2017)
- [On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Data](https://mlsanity.com/paper/1808.10585/) (2018)
- [Addressing the Loss-Metric Mismatch with Adaptive Loss Alignment](https://mlsanity.com/paper/1905.05895/) (2019)
- [An Effective Label Noise Model for DNN Text Classification](https://mlsanity.com/paper/1903.07507/) (2019)
- [A Regularization Approach for Instance-Based Superset Label Learning](https://mlsanity.com/paper/1904.02832/) (2019)
- [AutoLoss: Learning Discrete Schedules for Alternate Optimization](https://mlsanity.com/paper/1810.02442/) (2018)
- [Adversarial Partial Multi-Label Learning](https://mlsanity.com/paper/1909.06717/) (2019)

## Built on by (most cited first, 9 of 9)

- [Regularly Truncated M-estimators for Learning with Noisy Labels](https://mlsanity.com/paper/2309.00894/) (2023)
- [Counterfactual Reasoning for Multi-Label Image Classification via Patching-Based Training](https://mlsanity.com/paper/2404.06287/) (2024)
- [Rethinking Consistent Multi-Label Classification Under Inexact Supervision](https://mlsanity.com/paper/2510.04091/) (2025)
- [What killed the Convex Booster ?](https://mlsanity.com/paper/2205.09628/) (2022)
- [A Robust Multilabel Method Integrating Rule-based Transparent Model, Soft Label Correlation Learning and Label Noise Resistance](https://mlsanity.com/paper/2301.03283/) (2023)
- [Multi-Label Noise Transition Matrix Estimation with Label Correlations: Theory and Algorithm](https://mlsanity.com/paper/2309.12706/) (2023)
- [When the Small-Loss Trick is Not Enough: Multi-Label Image Classification with Noisy Labels Applied to CCTV Sewer Inspections](https://mlsanity.com/paper/2410.07689/) (2024)
- [MoMBS: Mixed-order minibatch sampling enhances model training from diverse-quality images](https://mlsanity.com/paper/2505.18741/) (2025)
- [Adaptive Gradient Calibration for Single-Positive Multi-Label Learning in Remote Sensing Image Scene Classification](https://mlsanity.com/paper/2510.08269/) (2025)

## Abstract (arXiv)

Class-conditional noise commonly exists in machine learning tasks, where the class label is corrupted with a probability depending on its ground-truth. Many research efforts have been made to improve the model robustness against the class-conditional noise. However, they typically focus on the single label case by assuming that only one label is corrupted. In real applications, an instance is usually associated with multiple labels, which could be corrupted simultaneously with their respective conditional probabilities. In this paper, we formalize this problem as a general framework of learning with Class-Conditional Multi-label Noise (CCMN for short). We establish two unbiased estimators with error bounds for solving the CCMN problems, and further prove that they are consistent with commonly used multi-label loss functions. Finally, a new method for partial multi-label learning is implemented with unbiased estimator under the CCMN framework. Empirical studies on multiple datasets and various evaluation metrics validate the effectiveness of the proposed method.