# Multi-class Classification from Multiple Unlabeled Datasets with Partial Risk Regularization

arXiv: https://arxiv.org/abs/2207.01555 · HTML: https://mlsanity.com/paper/2207.01555/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 4 Jul 2022.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Do We Need Zero Training Loss After Achieving Zero Training Error?](https://mlsanity.com/paper/2002.08709/) (2020)
- [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)
- [Learning from Label Proportions with Consistency Regularization](https://mlsanity.com/paper/1910.13188/) (2019)
- [Mitigating Overfitting in Supervised Classification from Two Unlabeled Datasets: A Consistent Risk Correction Approach](https://mlsanity.com/paper/1910.08974/) (2019)
- [Learning from Label Proportions with Generative Adversarial Networks](https://mlsanity.com/paper/1909.02180/) (2019)
- [proptoSVM for learning with label proportions](https://mlsanity.com/paper/1306.0886/) (2013)

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

- [A General Framework for Learning from Weak Supervision](https://mlsanity.com/paper/2402.01922/) (2024)
- [Boosting Prompt-Based Self-Training With Mapping-Free Automatic Verbalizer for Multi-Class Classification](https://mlsanity.com/paper/2312.04982/) (2023)
- [Learning from M-Tuple Dominant Positive and Unlabeled Data](https://mlsanity.com/paper/2506.15686/) (2025)
- [A Unified and Stable Risk Minimization Framework for Weakly Supervised Learning with Theoretical Guarantees](https://mlsanity.com/paper/2511.22823/) (2025)
- [Generalized Distribution-Free Semi-Supervised Learning with Risk Rewrite](https://mlsanity.com/paper/2607.11947/) (2026)
- [Multiclass Classification without Labels via Posterior Simplex Geometry](https://mlsanity.com/paper/2607.24943/) (2026)

## Abstract (arXiv)

Recent years have witnessed a great success of supervised deep learning, where predictive models were trained from a large amount of fully labeled data. However, in practice, labeling such big data can be very costly and may not even be possible for privacy reasons. Therefore, in this paper, we aim to learn an accurate classifier without any class labels. More specifically, we consider the case where multiple sets of unlabeled data and only their class priors, i.e., the proportions of each class, are available. Under this problem setup, we first derive an unbiased estimator of the classification risk that can be estimated from the given unlabeled sets and theoretically analyze the generalization error of the learned classifier. We then find that the classifier obtained as such tends to cause overfitting as its empirical risks go negative during training. To prevent overfitting, we further propose a partial risk regularization that maintains the partial risks with respect to unlabeled datasets and classes to certain levels. Experiments demonstrate that our method effectively mitigates overfitting and outperforms state-of-the-art methods for learning from multiple unlabeled sets.