提出三维度理论框架，解释二分类不平衡的衰减机制。
A Theoretical and Empirical Taxonomy of Imbalance in Binary Classification
- 用η、κ、Δ三尺度构建统一理论模型
- 实验证明少数类召回率在log(η)>Δ√κ时骤降
- 适用于各类模型，可指导不平衡场景应对
类别不平衡严重降低分类性能，但其影响缺乏统一理论分析。我们基于三个基本尺度——不平衡系数η、样本-维度比κ和内在可分性Δ——提出一个严谨框架。从高斯贝叶斯分类器出发，推导出闭式贝叶斯误差，揭示不平衡如何移动判别边界，产生可预测的四类退化模式：正常、轻度、极端与灾难性。利用一个平衡的高维基因组数据集，仅改变η而固定κ与Δ。在参数与非参数模型中，实证结果均紧密符合理论预测：当log(η)超过Δ√κ时，少数类召回率急剧下降；精确率不对称上升；F1分数与PR-AUC随预测退化模式同步下降。结果表明，三元组(η,κ,Δ)提供了模型无关、几何基础明确的不平衡退化解释。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。