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杰弗里斯中心的快速代理中心:杰弗里斯-费舍尔-拉奥中心和高斯-布雷格曼感应中心
1Sony Computer Science Laboratories, Tokyo 141-0022, Japan.
Entropy (Basel, Switzerland)
|January 8, 2025
概括
新的Jeffreys-Fisher-Rao和Gauss-Bregman中心为Jeffreys中心体提供了实用,封闭形式的近似,这是概率分布分析中的一个关键措施. 这些方法提高了诸如集群和信息检索等任务的计算效率.
科学领域:
- 信息几何学信息几何学
- 统计推理 统计推理
- 机器学习 机器学习
背景情况:
- 杰弗里斯中间体,一个对称的库尔巴克-莱布勒中间体,对于概率分布的中心性至关重要.
- 对于Jeffreys中位数的现有数值近似,对于分类和多变量正常分布来说,计算密集.
- 在实际应用中,需要有效的,封闭形式的替代品来替代杰弗里斯的中间体.
研究的目的:
- 介绍杰弗里斯-费舍尔-拉奥中心作为杰弗里斯中心体的封闭形式近似.
- 提出高斯 - 布雷格曼中心作为杰弗里斯中间体的归纳,收近似.
- 为了评估这些新中心的准确性和效率,与数值的杰弗里斯中间体相比.
主要方法:
- 定义Jeffreys-Fisher-Rao中心为侧面Kullback-Leibler中心体的Fisher-Rao中点. 定义Jeffreys-Fisher-Rao中心为侧面Kullback-Leibler中心体的Fisher-Rao中点.
- 通过对指数家族的高斯算术-几何平均值进行概括,开发了高斯-布雷格曼中心.
- 进行了实验,将拟议的中心与数值的杰弗里斯中间体进行比较,用于分类和正常分布.
主要成果:
- 杰弗里斯-费舍尔-拉奥中心提供了指数家族的通用公式和分类分布和正常分布的封闭形式解决方案.
- 高斯-布雷格曼中心表现出快速收,并且有效地接近杰弗里斯心脏.
- 实验结果显示,这两个新中心都非常接近杰弗里斯中心体,提供了显著的计算优势.
结论:
- 杰弗里斯-菲舍尔-拉奥和高斯-布雷格曼中心是杰弗里斯中心体的高效,封闭形式的代理.
- 这些新型中心提高了在信息检索,融合和集群中使用分布中心性的实用性.
- 这些发现在信息几何学中的双重平面空间框架内被重新解释.
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