# A Generalized Unbiased Risk Estimator for Learning with Augmented Classes

arXiv: https://arxiv.org/abs/2306.06894 · HTML: https://mlsanity.com/paper/2306.06894/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 12 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Recent Advances in Open Set Recognition: A Survey](https://mlsanity.com/paper/1811.08581/) (2018)
- [Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2004.10956/) (2020)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [The Extreme Value Machine](https://mlsanity.com/paper/1506.06112/) (2015)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Classification from Pairwise Similarity and Unlabeled Data](https://mlsanity.com/paper/1802.04381/) (2018)
- [Mitigating Overfitting in Supervised Classification from Two Unlabeled Datasets: A Consistent Risk Correction Approach](https://mlsanity.com/paper/1910.08974/) (2019)
- [Pointwise Binary Classification with Pairwise Confidence Comparisons](https://mlsanity.com/paper/2010.01875/) (2020)
- [An Unbiased Risk Estimator for Learning with Augmented Classes](https://mlsanity.com/paper/1910.09388/) (2019)
- [Distribution-Free One-Pass Learning](https://mlsanity.com/paper/1706.02471/) (2017)

## Built on by (most cited first, 2 of 2)

- [An Unbiased Risk Estimator for Partial Label Learning with Augmented Classes](https://mlsanity.com/paper/2409.19600/) (2024)
- [On the Learning with Augmented Class via Forests](https://mlsanity.com/paper/2505.09294/) (2025)

## Abstract (arXiv)

In contrast to the standard learning paradigm where all classes can be observed in training data, learning with augmented classes (LAC) tackles the problem where augmented classes unobserved in the training data may emerge in the test phase. Previous research showed that given unlabeled data, an unbiased risk estimator (URE) can be derived, which can be minimized for LAC with theoretical guarantees. However, this URE is only restricted to the specific type of one-versus-rest loss functions for multi-class classification, making it not flexible enough when the loss needs to be changed with the dataset in practice. In this paper, we propose a generalized URE that can be equipped with arbitrary loss functions while maintaining the theoretical guarantees, given unlabeled data for LAC. To alleviate the issue of negative empirical risk commonly encountered by previous studies, we further propose a novel risk-penalty regularization term. Experiments demonstrate the effectiveness of our proposed method.