Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.04149 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918276706074624 |
|---|---|
| author | Essomba, Rose Yvette Bandolo Fokoué, Ernest |
| author_facet | Essomba, Rose Yvette Bandolo Fokoué, Ernest |
| contents | 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 $κ$, and the intrinsic separability $Δ$. 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 $κ$ and $Δ$ fixed. Across parametric and non-parametric models, empirical degradation closely follows theoretical predictions: minority Recall collapses once $\log(η)$ exceeds $Δ\sqrtκ$, Precision increases asymmetrically, and F1-score and PR-AUC decline in line with the predicted regimes. These results show that the triplet $(η,κ,Δ)$ provides a model-agnostic, geometrically grounded explanation of imbalance-induced deterioration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04149 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Theoretical and Empirical Taxonomy of Imbalance in Binary Classification Essomba, Rose Yvette Bandolo Fokoué, Ernest Machine Learning 62H10, 62H30 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 $κ$, and the intrinsic separability $Δ$. 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 $κ$ and $Δ$ fixed. Across parametric and non-parametric models, empirical degradation closely follows theoretical predictions: minority Recall collapses once $\log(η)$ exceeds $Δ\sqrtκ$, Precision increases asymmetrically, and F1-score and PR-AUC decline in line with the predicted regimes. These results show that the triplet $(η,κ,Δ)$ provides a model-agnostic, geometrically grounded explanation of imbalance-induced deterioration. |
| title | A Theoretical and Empirical Taxonomy of Imbalance in Binary Classification |
| topic | Machine Learning 62H10, 62H30 |
| url | https://arxiv.org/abs/2601.04149 |