希尔伯特曲线投影距离用于分布比较
IEEE transactions on pattern analysis and machine intelligence
|February 8, 2024
概括
我们介绍了希尔伯特曲线投影 (HCP) 距离,这是一种用于比较概率分布的新度量. 这种低复杂度的方法有效地测量分布距离,在机器学习任务中表现优于现有的技术.
科学领域:
- 机器学习 机器学习
- 可能性理论概率理论.
- 数据分析 数据分析
背景情况:
- 分布比较对于机器学习任务如分类和生成建模至关重要.
- 现有的指标可能会受到高计算复杂性或高维空间的限制的影响.
研究的目的:
- 提出一种新的,低复杂度的度量来测量概率分布之间的距离.
- 介绍希尔伯特曲线投影 (HCP) 距离并分析其属性.
主要方法:
- 使用希尔伯特曲线预测高维概率分布以创建合.
- 根据衍生的合计算在原始空间中的运输距离.
- 使用子空间投影开发变体,以减轻维度的诅咒.
主要成果:
- 希尔伯特曲线投影 (HCP) 距离被证明是具有边界支的概率测量的适当度量.
- 经验性HCP距离以O的速度与其人口对应物相收 (n^{-1/2max{d,p}}).
- 医务人员距离变量有效地解决了维度的诅咒.
结论:
- 医疗人员距离为瓦斯斯坦距离提供了一个有效的,低复杂性的替代方案.
- 它克服了切片瓦瑟斯坦距离的局限性,显示出实际应用的希望.
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