# Sharp error bounds for imbalanced classification: how many examples in the minority class?

arXiv: https://arxiv.org/abs/2310.14826 · HTML: https://mlsanity.com/paper/2310.14826/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 73 references that are in the map.
- First posted on arXiv 23 Oct 2023.

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

- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Cost Sensitive Learning of Deep Feature Representations from Imbalanced Data](https://mlsanity.com/paper/1508.03422/) (2015)
- [BAGAN: Data Augmentation with Balancing GAN](https://mlsanity.com/paper/1803.09655/) (2018)
- [Fast rates in statistical and online learning](https://mlsanity.com/paper/1507.02592/) (2015)
- [Stability and Deviation Optimal Risk Bounds with Convergence Rate O(1/n)](https://mlsanity.com/paper/2103.12024/) (2021)
- [Class-Weighted Classification: Trade-offs and Robust Approaches](https://mlsanity.com/paper/2005.12914/) (2020)
- [When OT meets MoM: Robust estimation of Wasserstein Distance](https://mlsanity.com/paper/2006.10325/) (2020)
- [Nearest Neighbour Based Estimates of Gradients: Sharp Nonasymptotic Bounds and Applications](https://mlsanity.com/paper/2006.15043/) (2020)
- [Risk-consistency of cross-validation with lasso-type procedures](https://mlsanity.com/paper/1308.0810/) (2013)
- [Risk bounds when learning infinitely many response functions by ordinary linear regression](https://mlsanity.com/paper/2006.09223/) (2020)

## Built on by (most cited first, 4 of 4)

- [Do we need rebalancing strategies? A theoretical and empirical study around SMOTE and its variants](https://mlsanity.com/paper/2402.03819/) (2024)
- [Concentration and excess risk bounds for imbalanced classification with synthetic oversampling](https://mlsanity.com/paper/2510.20472/) (2025)
- [Algorithmic Accountability in Small Data: Sample-Size-Induced Bias Within Classification Metrics](https://mlsanity.com/paper/2505.03992/) (2025)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)

## Abstract (arXiv)

When dealing with imbalanced classification data, reweighting the loss function is a standard procedure allowing to equilibrate between the true positive and true negative rates within the risk measure. Despite significant theoretical work in this area, existing results do not adequately address a main challenge within the imbalanced classification framework, which is the negligible size of one class in relation to the full sample size and the need to rescale the risk function by a probability tending to zero. To address this gap, we present two novel contributions in the setting where the rare class probability approaches zero: (1) a non asymptotic fast rate probability bound for constrained balanced empirical risk minimization, and (2) a consistent upper bound for balanced nearest neighbors estimates. Our findings provide a clearer understanding of the benefits of class-weighting in realistic settings, opening new avenues for further research in this field.