# Learning from Positive and Unlabeled Data with Augmented Classes

arXiv: https://arxiv.org/abs/2207.13274 · HTML: https://mlsanity.com/paper/2207.13274/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 27 Jul 2022.

## Builds on (most cited first, 16 of 16)

- [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)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Data](https://mlsanity.com/paper/1808.10585/) (2018)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [Classification from Pairwise Similarity and Unlabeled Data](https://mlsanity.com/paper/1802.04381/) (2018)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [On the Consistency of Ordinal Regression Methods](https://mlsanity.com/paper/1408.2327/) (2014)
- [Binary Classification from Positive-Confidence Data](https://mlsanity.com/paper/1710.07138/) (2017)
- [Convex Calibration Dimension for Multiclass Loss Matrices](https://mlsanity.com/paper/1408.2764/) (2014)
- [Classification from Pairwise Similarities/Dissimilarities and Unlabeled Data via Empirical Risk Minimization](https://mlsanity.com/paper/1904.11717/) (2019)
- [An Embedding Framework for Consistent Polyhedral Surrogates](https://mlsanity.com/paper/1907.07330/) (2019)
- [On Positive-Unlabeled Classification in GAN](https://mlsanity.com/paper/2002.01136/) (2020)
- [An Unbiased Risk Estimator for Learning with Augmented Classes](https://mlsanity.com/paper/1910.09388/) (2019)
- [Efficient Training for Positive Unlabeled Learning](https://mlsanity.com/paper/1608.06807/) (2016)

## Built on by (most cited first, 1 of 1)

- [Learning from M-Tuple Dominant Positive and Unlabeled Data](https://mlsanity.com/paper/2506.15686/) (2025)

## Abstract (arXiv)

Positive Unlabeled (PU) learning aims to learn a binary classifier from only positive and unlabeled data, which is utilized in many real-world scenarios. However, existing PU learning algorithms cannot deal with the real-world challenge in an open and changing scenario, where examples from unobserved augmented classes may emerge in the testing phase. In this paper, we propose an unbiased risk estimator for PU learning with Augmented Classes (PUAC) by utilizing unlabeled data from the augmented classes distribution, which can be easily collected in many real-world scenarios. Besides, we derive the estimation error bound for the proposed estimator, which provides a theoretical guarantee for its convergence to the optimal solution. Experiments on multiple realistic datasets demonstrate the effectiveness of proposed approach.