# Bounding the Worst-class Error: A Boosting Approach

arXiv: https://arxiv.org/abs/2310.14890 · HTML: https://mlsanity.com/paper/2310.14890/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 20 Oct 2023.

## 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)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Influence-Balanced Loss for Imbalanced Visual Classification](https://mlsanity.com/paper/2110.02444/) (2021)
- [Identifying and Compensating for Feature Deviation in Imbalanced Deep Learning](https://mlsanity.com/paper/2001.01385/) (2020)
- [Label-Imbalanced and Group-Sensitive Classification under Overparameterization](https://mlsanity.com/paper/2103.01550/) (2021)
- [Why does Throwing Away Data Improve Worst-Group Error?](https://mlsanity.com/paper/2205.11672/) (2022)
- [Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Bound](https://mlsanity.com/paper/2106.12535/) (2021)
- [Simplified and Unified Analysis of Various Learning Problems by Reduction to Multiple-Instance Learning](https://mlsanity.com/paper/1911.05999/) (2019)

## Abstract (arXiv)

This paper tackles the problem of the worst-class error rate, instead of the standard error rate averaged over all classes. For example, a three-class classification task with class-wise error rates of 10%, 10%, and 40% has a worst-class error rate of 40%, whereas the average is 20% under the class-balanced condition. The worst-class error is important in many applications. For example, in a medical image classification task, it would not be acceptable for the malignant tumor class to have a 40% error rate, while the benign and healthy classes have a 10% error rates. To avoid overfitting in worst-class error minimization using Deep Neural Networks (DNNs), we design a problem formulation for bounding the worst-class error instead of achieving zero worst-class error. Moreover, to correctly bound the worst-class error, we propose a boosting approach which ensembles DNNs. We give training and generalization worst-class-error bound. Experimental results show that the algorithm lowers worst-class test error rates while avoiding overfitting to the training set. This code is available at https://github.com/saito-yuya/Bounding-the-Worst-class-error-A-Boosting-Approach.