# Learning with Proper Partial Labels

arXiv: https://arxiv.org/abs/2112.12303 · HTML: https://mlsanity.com/paper/2112.12303/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 23 Dec 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Progressive Identification of True Labels for Partial-Label Learning](https://mlsanity.com/paper/2002.08053/) (2020)
- [Learning with Biased Complementary Labels](https://mlsanity.com/paper/1711.09535/) (2017)
- [Masking: A New Perspective of Noisy Supervision](https://mlsanity.com/paper/1805.08193/) (2018)
- [Provably Consistent Partial-Label Learning](https://mlsanity.com/paper/2007.08929/) (2020)
- [Learning from Complementary Labels](https://mlsanity.com/paper/1705.07541/) (2017)
- [Leveraged Weighted Loss for Partial Label Learning](https://mlsanity.com/paper/2106.05731/) (2021)
- [Confidence Scores Make Instance-dependent Label-noise Learning Possible](https://mlsanity.com/paper/2001.03772/) (2020)
- [Complementary-Label Learning for Arbitrary Losses and Models](https://mlsanity.com/paper/1810.04327/) (2018)
- [On Symmetric Losses for Learning from Corrupted Labels](https://mlsanity.com/paper/1901.09314/) (2019)
- [Learning with Multiple Complementary Labels](https://mlsanity.com/paper/1912.12927/) (2019)
- [On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Data](https://mlsanity.com/paper/1808.10585/) (2018)
- [Classification from Pairwise Similarity and Unlabeled Data](https://mlsanity.com/paper/1802.04381/) (2018)
- [Binary Classification from Positive-Confidence Data](https://mlsanity.com/paper/1710.07138/) (2017)
- [Pointwise Binary Classification with Pairwise Confidence Comparisons](https://mlsanity.com/paper/2010.01875/) (2020)
- [Learning from Similarity-Confidence Data](https://mlsanity.com/paper/2102.06879/) (2021)
- [Multi-Class Classification from Single-Class Data with Confidences](https://mlsanity.com/paper/2106.08864/) (2021)

## Built on by (most cited first, 8 of 8)

- [Progressive Purification for Instance-Dependent Partial Label Learning](https://mlsanity.com/paper/2206.00830/) (2022)
- [Realistic Evaluation of Deep Partial-Label Learning Algorithms](https://mlsanity.com/paper/2502.10184/) (2025)
- [Towards Effective Visual Representations for Partial-Label Learning](https://mlsanity.com/paper/2305.06080/) (2023)
- [Imprecise Label Learning: A Unified Framework for Learning with Various Imprecise Label Configurations](https://mlsanity.com/paper/2305.12715/) (2023)
- [Unified Risk Analysis for Weakly Supervised Learning](https://mlsanity.com/paper/2309.08216/) (2023)
- [Learning from Label Proportions with Instance-wise Consistency](https://mlsanity.com/paper/2203.12836/) (2022)
- [A Unified and Stable Risk Minimization Framework for Weakly Supervised Learning with Theoretical Guarantees](https://mlsanity.com/paper/2511.22823/) (2025)
- [Recent advances in weakly supervised learning: New supervision paradigms, assumption relaxations, and practical solutions](https://mlsanity.com/paper/2608.06896/) (2026)

## Abstract (arXiv)

Partial-label learning is a kind of weakly-supervised learning with inexact labels, where for each training example, we are given a set of candidate labels instead of only one true label. Recently, various approaches on partial-label learning have been proposed under different generation models of candidate label sets. However, these methods require relatively strong distributional assumptions on the generation models. When the assumptions do not hold, the performance of the methods is not guaranteed theoretically. In this paper, we propose the notion of properness on partial labels. We show that this proper partial-label learning framework requires a weaker distributional assumption and includes many previous partial-label learning settings as special cases. We then derive a unified unbiased estimator of the classification risk. We prove that our estimator is risk-consistent, and we also establish an estimation error bound. Finally, we validate the effectiveness of our algorithm through experiments.