# Learning from Ambiguous Data with Hard Labels

arXiv: https://arxiv.org/abs/2501.01844 · HTML: https://mlsanity.com/paper/2501.01844/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 3 Jan 2025.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [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)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks](https://mlsanity.com/paper/2103.14749/) (2021)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Human uncertainty makes classification more robust](https://mlsanity.com/paper/1908.07086/) (2019)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [A Survey of Label-noise Representation Learning: Past, Present and Future](https://mlsanity.com/paper/2011.04406/) (2020)
- [Re-labeling ImageNet: from Single to Multi-Labels, from Global to Localized Labels](https://mlsanity.com/paper/2101.05022/) (2021)
- [Learning From Noisy Large-Scale Datasets With Minimal Supervision](https://mlsanity.com/paper/1701.01619/) (2017)
- [Understanding and Improving Early Stopping for Learning with Noisy Labels](https://mlsanity.com/paper/2106.15853/) (2021)
- [A Survey on Data Collection for Machine Learning: a Big Data -- AI Integration Perspective](https://mlsanity.com/paper/1811.03402/) (2018)
- [Deep Label Distribution Learning with Label Ambiguity](https://mlsanity.com/paper/1611.01731/) (2016)
- [Generalized Jensen-Shannon Divergence Loss for Learning with Noisy Labels](https://mlsanity.com/paper/2105.04522/) (2021)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [Artificial Neural Variability for Deep Learning: On Overfitting, Noise Memorization, and Catastrophic Forgetting](https://mlsanity.com/paper/2011.06220/) (2020)
- [Positive-Negative Momentum: Manipulating Stochastic Gradient Noise to Improve Generalization](https://mlsanity.com/paper/2103.17182/) (2021)
- [Learning Soft Labels via Meta Learning](https://mlsanity.com/paper/2009.09496/) (2020)
- [Sparse Double Descent: Where Network Pruning Aggravates Overfitting](https://mlsanity.com/paper/2206.08684/) (2022)
- [Estimating the class prior and posterior from noisy positives and unlabeled data](https://mlsanity.com/paper/1606.08561/) (2016)
- [Rethinking Class-Prior Estimation for Positive-Unlabeled Learning](https://mlsanity.com/paper/2002.03673/) (2020)

## Abstract (arXiv)

Real-world data often contains intrinsic ambiguity that the common single-hard-label annotation paradigm ignores. Standard training using ambiguous data with these hard labels may produce overly confident models and thus leading to poor generalization. In this paper, we propose a novel framework called Quantized Label Learning (QLL) to alleviate this issue. First, we formulate QLL as learning from (very) ambiguous data with hard labels: ideally, each ambiguous instance should be associated with a ground-truth soft-label distribution describing its corresponding probabilistic weight in each class, however, this is usually not accessible; in practice, we can only observe a quantized label, i.e., a hard label sampled (quantized) from the corresponding ground-truth soft-label distribution, of each instance, which can be seen as a biased approximation of the ground-truth soft-label. Second, we propose a Class-wise Positive-Unlabeled (CPU) risk estimator that allows us to train accurate classifiers from only ambiguous data with quantized labels. Third, to simulate ambiguous datasets with quantized labels in the real world, we design a mixing-based ambiguous data generation procedure for empirical evaluation. Experiments demonstrate that our CPU method can significantly improve model generalization performance and outperform the baselines.