基于广义线性模型的不平衡分类最优下采样
Optimal Downsampling for Imbalanced Classification with Generalized Linear Models
AI总结：
针对大规模高度不平衡分类的下采样问题，提出基于广义线性模型的伪极大似然估计量，推导其渐近正态性与理论保证，给出兼顾统计精度和计算效率的最优下采样率，实验验证其性能优于现有常用方法。
摘要：
下采样（欠采样）是用于大规模、高度不平衡分类模型的一种技术。我们研究了使用广义线性模型（GLMs）进行不平衡分类的最优下采样问题。我们提出了一种伪极大似然估计量，并在总体不平衡程度随样本量增大而加剧的语境下研究了其渐近正态性，为该估计量提供了理论保证。此外，我们通过平衡统计准确性与计算效率的准则计算出最优下采样率。我们在合成数据与实证数据上开展的数值实验进一步验证了理论结果，并表明所提出的估计量优于常用的替代方法。
英文摘要：
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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