# Why does Throwing Away Data Improve Worst-Group Error?

arXiv: https://arxiv.org/abs/2205.11672 · HTML: https://mlsanity.com/paper/2205.11672/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 23 May 2022.

## Builds on (most cited first, 10 of 10)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Simple data balancing achieves competitive worst-group-accuracy](https://mlsanity.com/paper/2110.14503/) (2021)
- [Understanding the Failure Modes of Out-of-Distribution Generalization](https://mlsanity.com/paper/2010.15775/) (2020)
- [Loss minimization and parameter estimation with heavy tails](https://mlsanity.com/paper/1307.1827/) (2013)
- [Multi-group Agnostic PAC Learnability](https://mlsanity.com/paper/2105.09989/) (2021)
- [Simple and near-optimal algorithms for hidden stratification and multi-group learning](https://mlsanity.com/paper/2112.12181/) (2021)

## Built on by (most cited first, 22 of 22)

- [The Clever Hans Mirage: A Comprehensive Survey on Spurious Correlations in Machine Learning](https://mlsanity.com/paper/2402.12715/) (2024)
- [On Provable Length and Compositional Generalization](https://mlsanity.com/paper/2402.04875/) (2024)
- [The Data Addition Dilemma](https://mlsanity.com/paper/2408.04154/) (2024)
- [Phi-4-reasoning-vision-15B Technical Report](https://mlsanity.com/paper/2603.03975/) (2026)
- [Understanding Domain Generalization: A Noise Robustness Perspective](https://mlsanity.com/paper/2401.14846/) (2024)
- [Robustness to Subpopulation Shift with Domain Label Noise via Regularized Annotation of Domains](https://mlsanity.com/paper/2402.11039/) (2024)
- [DRoP: Distributionally Robust Data Pruning](https://mlsanity.com/paper/2404.05579/) (2024)
- [Restoring balance: principled under/oversampling of data for optimal classification](https://mlsanity.com/paper/2405.09535/) (2024)
- [The Group Robustness is in the Details: Revisiting Finetuning under Spurious Correlations](https://mlsanity.com/paper/2407.13957/) (2024)
- [Do we need rebalancing strategies? A theoretical and empirical study around SMOTE and its variants](https://mlsanity.com/paper/2402.03819/) (2024)
- [The Impact of Coreset Selection on Spurious Correlations and Group Robustness](https://mlsanity.com/paper/2507.11690/) (2025)
- [Theoretical Guarantees of Data Augmented Last Layer Retraining Methods](https://mlsanity.com/paper/2405.05934/) (2024)
- [Minority Collective Action for User-Side Fairness](https://mlsanity.com/paper/2508.15374/) (2025)
- [On the Unreasonable Effectiveness of Last-layer Retraining](https://mlsanity.com/paper/2512.01766/) (2025)
- [Generalizing to any diverse distribution: uniformity, gentle finetuning and rebalancing](https://mlsanity.com/paper/2410.05980/) (2024)
- [Thumb on the Scale: Optimal Loss Weighting in Last Layer Retraining](https://mlsanity.com/paper/2506.20025/) (2025)
- [On Measuring Localization of Shortcuts in Deep Networks](https://mlsanity.com/paper/2510.26560/) (2025)
- [LT-Soups: Bridging Head and Tail Classes via Subsampled Model Soups](https://mlsanity.com/paper/2511.10683/) (2025)
- [Bounding the Worst-class Error: A Boosting Approach](https://mlsanity.com/paper/2310.14890/) (2023)
- [Label Noise Robustness for Domain-Agnostic Fair Corrections via Nearest Neighbors Label Spreading](https://mlsanity.com/paper/2406.09561/) (2024)
- [On Imbalanced Regression with Hoeffding Trees](https://mlsanity.com/paper/2602.22101/) (2026)
- [DeconDTN-Toolkit: A Library for Evaluation and Enhancement of Robustness to Provenance Shift](https://mlsanity.com/paper/2605.11237/) (2026)

## Abstract (arXiv)

When facing data with imbalanced classes or groups, practitioners follow an intriguing strategy to achieve best results. They throw away examples until the classes or groups are balanced in size, and then perform empirical risk minimization on the reduced training set. This opposes common wisdom in learning theory, where the expected error is supposed to decrease as the dataset grows in size. In this work, we leverage extreme value theory to address this apparent contradiction. Our results show that the tails of the data distribution play an important role in determining the worst-group-accuracy of linear classifiers. When learning on data with heavy tails, throwing away data restores the geometric symmetry of the resulting classifier, and therefore improves its worst-group generalization.