提出最优下采样方法，提升不平衡分类中GLM的准确性和效率。
Optimal Downsampling for Imbalanced Classification with Generalized Linear Models
- 基于伪最大似然估计，适配极端不平衡数据场景
- 理论证明估计量渐近正态，且可优化采样率平衡精度与效率
- 在合成与真实数据上优于常见方法，适合高偏差数据建模
下采样是处理大规模高度不平衡分类问题的常用技术。本文研究广义线性模型（GLMs）在不平衡分类中的最优下采样策略。提出一种伪最大似然估计器，并在样本量趋于无穷而类别分布日益不平衡的条件下，分析其渐近正态性。给出了该估计器的理论保证。同时，基于统计精度与计算效率的权衡准则，推导出最优下采样率。数值实验在合成数据和实际数据上验证了理论结果，表明所提估计器显著优于现有常用方法。
原文摘要 · Abstract (English)
Downsampling or under-sampling is a technique that is utilized in the context of large and highly imbalanced classification models. We study optimal downsampling for imbalanced classification using generalized linear models (GLMs). We propose a pseudo maximum likelihood estimator and study its asymptotic normality in the context of increasingly imbalanced populations relative to an increasingly large sample size. We provide theoretical guarantees for the introduced estimator. Additionally, we compute the optimal downsampling rate using a criterion that balances statistical accuracy and computational efficiency. Our numerical experiments, conducted on both synthetic and empirical data, further validate our theoretical results, and demonstrate that the introduced estimator outperforms commonly available alternatives.
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