# Imprecise Label Learning: A Unified Framework for Learning with Various Imprecise Label Configurations

arXiv: https://arxiv.org/abs/2305.12715 · HTML: https://mlsanity.com/paper/2305.12715/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 82 of its 150 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 30 of 82)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (2018)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)

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

- [Understanding and Mitigating the Label Noise in Pre-training on Downstream Tasks](https://mlsanity.com/paper/2309.17002/) (2023)
- [Slight Corruption in Pre-training Data Makes Better Diffusion Models](https://mlsanity.com/paper/2405.20494/) (2024)
- [Label Noise: Ignorance Is Bliss](https://mlsanity.com/paper/2411.00079/) (2024)
- [Impact of Noisy Supervision in Foundation Model Learning](https://mlsanity.com/paper/2403.06869/) (2024)
- [A General Framework for Learning from Weak Supervision](https://mlsanity.com/paper/2402.01922/) (2024)
- [Distilling Calibration via Conformalized Credal Inference](https://mlsanity.com/paper/2501.06066/) (2025)
- [Weakly-Supervised Contrastive Learning for Imprecise Class Labels](https://mlsanity.com/paper/2505.22028/) (2025)
- [Learning Robust Diffusion Models from Imprecise Supervision](https://mlsanity.com/paper/2510.03016/) (2025)
- [RIVET: Robust Idempotent Voice Attribute Editing](https://mlsanity.com/paper/2606.19629/) (2026)

## Abstract (arXiv)

Learning with reduced labeling standards, such as noisy label, partial label, and multiple label candidates, which we generically refer to as textitimprecise labels, is a commonplace challenge in machine learning tasks. Previous methods tend to propose specific designs for every emerging imprecise label configuration, which is usually unsustainable when multiple configurations of imprecision coexist. In this paper, we introduce imprecise label learning (ILL), a framework for the unification of learning with various imprecise label configurations. ILL leverages expectation-maximization (EM) for modeling the imprecise label information, treating the precise labels as latent variables.Instead of approximating the correct labels for training, it considers the entire distribution of all possible labeling entailed by the imprecise information. We demonstrate that ILL can seamlessly adapt to partial label learning, semi-supervised learning, noisy label learning, and, more importantly, a mixture of these settings. Notably, ILL surpasses the existing specified techniques for handling imprecise labels, marking the first unified framework with robust and effective performance across various challenging settings. We hope our work will inspire further research on this topic, unleashing the full potential of ILL in wider scenarios where precise labels are expensive and complicated to obtain.