A Theoretical and Empirical Taxonomy of Imbalance in Binary Classification
This work provides a model-agnostic, geometrically grounded explanation for imbalance effects, which is incremental as it builds on existing theoretical perspectives to unify analysis.
The authors tackled the problem of class imbalance degrading classification performance by proposing a theoretical framework based on three scales (imbalance coefficient, sample-dimension ratio, and intrinsic separability), showing that empirical degradation in metrics like Recall and F1-score closely follows predicted regimes such as Normal, Mild, Extreme, and Catastrophic.
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.