二进制回归和分类与共变量在米制空间
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1National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing, 401331, China.
Biometrics
|September 19, 2025
概括
我们开发了一个新的回归模型和对二进制数据的分类器,其中的共变量在米制空间中. 我们的方法提供最佳的估计和分类性能,通过模拟和fMRI数据分析证明了这一点.
科学领域:
- 统计 统计 统计 统计
- 机器学习 机器学习
- 数据科学数据科学数据科学
背景情况:
- 传统的回归模型假定矢量空间共变量.
- 尺度空间缺乏固有的向量结构,这对标准的统计方法构成挑战.
- 分析二进制响应与度量空间共变量需要新的方法.
研究的目的:
- 介绍一个新的回归模型,用于二进制响应与米制空间共变量.
- 开发一个针对尺度空间估值数据量身定制的二进制分类器.
- 建立理论性能界限,并证明实际效用.
主要方法:
- 提出了一种以逻辑回归为灵感的模型,用于度量空间数据.
- 开发了一个回归系数的最大概率估计器.
- 通过使用米度来计算估计误差的上下限.
- 对于一般的度量空间和里曼的多元体建立了最佳性.
主要成果:
- 建议的估计器在常见的度量空间中实现了最佳性能.
- 一个精细的边界在里曼的多样性上证明了分类器的最佳性.
- 这些方法是第一个在一般的度量空间中进行二进制响应分析的方法.
- 模拟研究证实了估计器和分类器的数值性能.
结论:
- 新的回归模型和分类器有效地处理二进制数据,其中具有米制空间共变量.
- 理论界限证实了拟议方法的统计效率和最佳性.
- 这种方法对神经成像分析 (fMRI) 等应用具有前景.
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