# A Theoretical and Empirical Taxonomy of Imbalance in Binary Classification

arXiv: https://arxiv.org/abs/2601.04149 · HTML: https://mlsanity.com/paper/2601.04149/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Builds on (most cited first, 8 of 8)

- [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)
- [A modern maximum-likelihood theory for high-dimensional logistic regression](https://mlsanity.com/paper/1803.06964/) (2018)
- [DeepSMOTE: Fusing Deep Learning and SMOTE for Imbalanced Data](https://mlsanity.com/paper/2105.02340/) (2021)
- [A survey on learning from imbalanced data streams: taxonomy, challenges, empirical study, and reproducible experimental framework](https://mlsanity.com/paper/2204.03719/) (2022)
- [A review of ensemble learning and data augmentation models for class imbalanced problems: combination, implementation and evaluation](https://mlsanity.com/paper/2304.02858/) (2023)
- [A Theoretical Analysis of the Learning Dynamics under Class Imbalance](https://mlsanity.com/paper/2207.00391/) (2022)
- [The harms of class imbalance corrections for machine learning based prediction models: a simulation study](https://mlsanity.com/paper/2404.19494/) (2024)

## Abstract (arXiv)

Class imbalance significantly degrades classification performance, yet its effects are rarely analyzed from a unified theoretical perspective. We propose a principled framework based on three fundamental scales: the imbalance coefficient η, the sample--dimension ratio kappa, and the intrinsic separability Delta. Starting from the Gaussian Bayes classifier, we derive closed-form Bayes errors and show how imbalance shifts the discriminant boundary, yielding a deterioration slope that predicts four regimes: Normal, Mild, Extreme, and Catastrophic. Using a balanced high-dimensional genomic dataset, we vary only η while keeping kappa and Delta fixed. Across parametric and non-parametric models, empirical degradation closely follows theoretical predictions: minority Recall collapses once log(η) exceeds Delta√kappa, Precision increases asymmetrically, and F1-score and PR-AUC decline in line with the predicted regimes. These results show that the triplet (η,kappa,Delta) provides a model-agnostic, geometrically grounded explanation of imbalance-induced deterioration.