计算不平衡分布之间的距离:平面度量法
Henri Schmidt1, Christian Düll1
1Institute of Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany.
概括
我们为平面度量引入了一种新的计算方法,即对于总质量不平等的分布来说,一个通用的瓦瑟斯坦距离. 这种方法对于不平衡的最佳运输和数据分析是有价值的,当规范化是不可行的.
科学领域:
- 计算数学是指计算数学.
- 机器学习是机器学习.
- 最佳运输理论的最佳运输理论.
背景情况:
- 瓦瑟斯坦距离 (W1) 是比较概率分布的一个基本度量.
- 现有的方法通常要求分布具有相同的总质量,从而限制了它们的适用性.
- 不平衡的最佳运输和数据分析任务往往涉及不同样本大小的分布或无法正常化的分布.
研究的目的:
- 为计算任意维度的平面度量提供一个强大的实现.
- 将最佳运输指标的实用性扩展到具有不平等总质量的场景.
- 开发一种能够根据质量差异区分分布的方法.
主要方法:
- 核心方法采用神经网络来确定最佳的测试功能.
- 这个测试函数用于计算平面度量,也称为双边界利普希茨距离.
- 重点是确保从独立训练的神经网络计算的距离的可比性.
主要成果:
- 实现成功计算了各个维度的平面度量.
- 该方法有效地适应并利用分布之间的质量差异.
- 使用地面真相和模拟数据进行实验验证,证明了计算距离的质量.
结论:
- 开发的实现为计算平面度量提供了一个实用的解决方案,将瓦瑟斯坦距离概括为.
- 这种工具对于不平衡的最佳运输问题以及对现实世界数据分布的分析特别重要.
- 该方法提供了一种可靠的方式来比较分布,即使它们具有不平等的总质量或无法正常化.
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