# Learning from Noisy Labels via Conditional Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2411.17113 · HTML: https://mlsanity.com/paper/2411.17113/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 26 Nov 2024.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Joint Optimization Framework for Learning with Noisy Labels](https://mlsanity.com/paper/1803.11364/) (2018)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Learning From Noisy Labels By Regularized Estimation Of Annotator Confusion](https://mlsanity.com/paper/1902.03680/) (2019)
- [Deep learning from crowds](https://mlsanity.com/paper/1709.01779/) (2017)
- [Who Said What: Modeling Individual Labelers Improves Classification](https://mlsanity.com/paper/1703.08774/) (2017)
- [Error-Bounded Correction of Noisy Labels](https://mlsanity.com/paper/2011.10077/) (2020)
- [Learning From Noisy Singly-labeled Data](https://mlsanity.com/paper/1712.04577/) (2017)
- [Pre-Train Your Loss: Easy Bayesian Transfer Learning with Informative Priors](https://mlsanity.com/paper/2205.10279/) (2022)
- [Mitigating Memorization of Noisy Labels by Clipping the Model Prediction](https://mlsanity.com/paper/2212.04055/) (2022)
- [Learning from Crowds by Modeling Common Confusions](https://mlsanity.com/paper/2012.13052/) (2020)
- [Max-MIG: an Information Theoretic Approach for Joint Learning from Crowds](https://mlsanity.com/paper/1905.13436/) (2019)
- [Error Rate Bounds and Iterative Weighted Majority Voting for Crowdsourcing](https://mlsanity.com/paper/1411.4086/) (2014)
- [Learning Supervised Topic Models for Classification and Regression from Crowds](https://mlsanity.com/paper/1808.05902/) (2018)
- [Deep Learning From Crowdsourced Labels: Coupled Cross-entropy Minimization, Identifiability, and Regularization](https://mlsanity.com/paper/2306.03288/) (2023)
- [Coupled Confusion Correction: Learning from Crowds with Sparse Annotations](https://mlsanity.com/paper/2312.07331/) (2023)

## Built on by (most cited first, 6 of 6)

- [When Priors Backfire: On the Vulnerability of Unlearnable Examples to Pretraining](https://mlsanity.com/paper/2603.04731/) (2026)
- [Full spectrum Unlearnable Examples via Spectral Equalization](https://mlsanity.com/paper/2606.26719/) (2026)
- [Optimal Fair Aggregation of Crowdsourced Noisy Labels using Demographic Parity Constraints](https://mlsanity.com/paper/2601.23221/) (2026)
- [crowd-hpo: Realistic Hyperparameter Optimization and Benchmarking for Learning from Crowds with Noisy Labels](https://mlsanity.com/paper/2504.09085/) (2025)
- [Combating Noisy Labels through Fostering Self- and Neighbor-Consistency](https://mlsanity.com/paper/2601.12795/) (2026)
- [Selective Posterior Margin Regularization for Forward-Corrected Classification](https://mlsanity.com/paper/2609.05859/) (2026)

## Abstract (arXiv)

While crowdsourcing has emerged as a practical solution for labeling large datasets, it presents a significant challenge in learning accurate models due to noisy labels from annotators with varying levels of expertise. Existing methods typically estimate the true label posterior, conditioned on the instance and noisy annotations, to infer true labels or adjust loss functions. These estimates, however, often overlook potential misspecification in the true label posterior, which can degrade model performances, especially in high-noise scenarios. To address this issue, we investigate learning from noisy annotations with an estimated true label posterior through the framework of conditional distributionally robust optimization (CDRO). We propose formulating the problem as minimizing the worst-case risk within a distance-based ambiguity set centered around a reference distribution. By examining the strong duality of the formulation, we derive upper bounds for the worst-case risk and develop an analytical solution for the dual robust risk for each data point. This leads to a novel robust pseudo-labeling algorithm that leverages the likelihood ratio test to construct a pseudo-empirical distribution, providing a robust reference probability distribution in CDRO. Moreover, to devise an efficient algorithm for CDRO, we derive a closed-form expression for the empirical robust risk and the optimal Lagrange multiplier of the dual problem, facilitating a principled balance between robustness and model fitting. Our experimental results on both synthetic and real-world datasets demonstrate the superiority of our method.