# Learning from M-Tuple Dominant Positive and Unlabeled Data

arXiv: https://arxiv.org/abs/2506.15686 · HTML: https://mlsanity.com/paper/2506.15686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 60 references that are in the map.
- First posted on arXiv 25 May 2025.

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

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Data](https://mlsanity.com/paper/1808.10585/) (2018)
- [On Learning from Label Proportions](https://mlsanity.com/paper/1402.5902/) (2014)
- [Classification from Pairwise Similarity and Unlabeled Data](https://mlsanity.com/paper/1802.04381/) (2018)
- [Weakly Supervised Learning with Side Information for Noisy Labeled Images](https://mlsanity.com/paper/2008.11586/) (2020)
- [Mitigating Overfitting in Supervised Classification from Two Unlabeled Datasets: A Consistent Risk Correction Approach](https://mlsanity.com/paper/1910.08974/) (2019)
- [Binary Classification from Positive-Confidence Data](https://mlsanity.com/paper/1710.07138/) (2017)
- [Classification from Pairwise Similarities/Dissimilarities and Unlabeled Data via Empirical Risk Minimization](https://mlsanity.com/paper/1904.11717/) (2019)
- [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)
- [Binary Classification with Confidence Difference](https://mlsanity.com/paper/2310.05632/) (2023)
- [Binary Classification from Multiple Unlabeled Datasets via Surrogate Set Classification](https://mlsanity.com/paper/2102.00678/) (2021)
- [Efficient Training for Positive Unlabeled Learning](https://mlsanity.com/paper/1608.06807/) (2016)
- [Impact of Noisy Supervision in Foundation Model Learning](https://mlsanity.com/paper/2403.06869/) (2024)
- [proptoSVM for learning with label proportions](https://mlsanity.com/paper/1306.0886/) (2013)
- [Multi-class Classification from Multiple Unlabeled Datasets with Partial Risk Regularization](https://mlsanity.com/paper/2207.01555/) (2022)
- [Multitask Weakly Supervised Learning for Origin Destination Travel Time Estimation](https://mlsanity.com/paper/2301.05336/) (2023)
- [Learning from Positive and Unlabeled Data with Augmented Classes](https://mlsanity.com/paper/2207.13274/) (2022)

## Abstract (arXiv)

Label Proportion Learning (LLP) addresses the classification problem where multiple instances are grouped into bags and each bag contains information about the proportion of each class. However, in practical applications, obtaining precise supervisory information regarding the proportion of instances in a specific class is challenging. To better align with real-world application scenarios and effectively leverage the proportional constraints of instances within tuples, this paper proposes a generalized learning framework MDPU. Specifically, we first mathematically model the distribution of instances within tuples of arbitrary size, under the constraint that the number of positive instances is no less than that of negative instances. Then we derive an unbiased risk estimator that satisfies risk consistency based on the empirical risk minimization (ERM) method. To mitigate the inevitable overfitting issue during training, a risk correction method is introduced, leading to the development of a corrected risk estimator. The generalization error bounds of the unbiased risk estimator theoretically demonstrate the consistency of the proposed method. Extensive experiments on multiple datasets and comparisons with other relevant baseline methods comprehensively validate the effectiveness of the proposed learning framework.