# An Unbiased Risk Estimator for Learning with Augmented Classes

arXiv: https://arxiv.org/abs/1910.09388 · HTML: https://mlsanity.com/paper/1910.09388/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2019.

## Built on by (most cited first, 13 of 13)

- [Open-environment Machine Learning](https://mlsanity.com/paper/2206.00423/) (2022)
- [Adapting to Online Label Shift with Provable Guarantees](https://mlsanity.com/paper/2207.02121/) (2022)
- [Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practical](https://mlsanity.com/paper/2311.15502/) (2023)
- [A Generalized Unbiased Risk Estimator for Learning with Augmented Classes](https://mlsanity.com/paper/2306.06894/) (2023)
- [Learning from Positive and Unlabeled Data with Augmented Classes](https://mlsanity.com/paper/2207.13274/) (2022)
- [Complementary Labels Learning with Augmented Classes](https://mlsanity.com/paper/2211.10701/) (2022)
- [An Unbiased Risk Estimator for Partial Label Learning with Augmented Classes](https://mlsanity.com/paper/2409.19600/) (2024)
- [Theoretically Guaranteed Distribution Adaptable Learning](https://mlsanity.com/paper/2411.02921/) (2024)
- [Learning from Concealed Labels](https://mlsanity.com/paper/2412.02230/) (2024)
- [ESA: Example Sieve Approach for Multi-Positive and Unlabeled Learning](https://mlsanity.com/paper/2412.02240/) (2024)
- [On the Learning with Augmented Class via Forests](https://mlsanity.com/paper/2505.09294/) (2025)
- [Scalable Class-Incremental Learning Based on Parametric Neural Collapse](https://mlsanity.com/paper/2512.21845/) (2025)
- [Recent advances in weakly supervised learning: New supervision paradigms, assumption relaxations, and practical solutions](https://mlsanity.com/paper/2608.06896/) (2026)

## Abstract (arXiv)

This paper studies the problem of learning with augmented classes (LAC), where augmented classes unobserved in the training data might emerge in the testing phase. Previous studies generally attempt to discover augmented classes by exploiting geometric properties, achieving inspiring empirical performance yet lacking theoretical understandings particularly on the generalization ability. In this paper we show that, by using unlabeled training data to approximate the potential distribution of augmented classes, an unbiased risk estimator of the testing distribution can be established for the LAC problem under mild assumptions, which paves a way to develop a sound approach with theoretical guarantees. Moreover, the proposed approach can adapt to complex changing environments where augmented classes may appear and the prior of known classes may change simultaneously. Extensive experiments confirm the effectiveness of our proposed approach.