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相关概念视频

Uniform Distribution01:19

Uniform Distribution

5.2K
The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular.
Two essential properties of this distribution are
5.2K
Central Limit Theorem01:14

Central Limit Theorem

15.9K
The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
15.9K
Distance Measurements by Taping01:18

Distance Measurements by Taping

100
Tapes are essential in surveying for accurate, durable, and short-distance measurements. Made from lightweight, nylon-coated steel, they offer flexibility and strength for rugged outdoor use. The nylon coating protects against rust and wear, extending the tape's life. Standard lengths, around 30 meters, are marked in meters and millimeters for precision.Surveyors select tapes based on site conditions and accuracy needs. Lightweight, nylon-coated tapes are commonly used for ease of handling and...
100
Construction of Frequency Distribution01:15

Construction of Frequency Distribution

8.2K
A frequency distribution table can be constructed using the steps given below.
First, make a table with two columns—one with the title of the data that needs to be organized, and the other column for frequency. [Draw a third column for tally marks if needed]. Then, take a look at the items given in the data set and decide if an ungrouped frequency distribution table or a grouped frequency distribution table would be more suitable. If there are large sets of different values, then it is...
8.2K
Applications of Normal Distribution01:22

Applications of Normal Distribution

5.6K
The normal distribution is a useful statistical tool. One of its practical applications is determining the door height after considering the normal distribution of heights of persons, such that many can pass through it easily without striking their heads. The normal distribution can also determine the probability of a person having a height less than a specific height.
The heights of 15 to 18-year-old males from Chile from 1984 to 1985 followed a normal distribution. The mean height is 172.36...
5.6K
Distance Corrections01:15

Distance Corrections

83
To achieve precise distance measurements, especially in surveying and construction, certain corrections must be applied to account for potential sources of error like the standardization errors, temperature variations, and slope adjustments.Standardization error emerges when measurement equipment undergoes changes, such as wear, repairs, or weather impacts. To address this, surveyors compare the equipment’s readings to a standard. This process identifies any deviation that might lead to...
83

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相关实验视频

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Computer-assisted Large-scale Visualization and Quantification of Pancreatic Islet Mass, Size Distribution and Architecture
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Computer-assisted Large-scale Visualization and Quantification of Pancreatic Islet Mass, Size Distribution and Architecture

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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.

Machine learning
|July 29, 2025
PubMed
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.
关键词:
双边界的利普希茨距离是双边界的.平面规范是平面规范.福特特 - 穆里耶距离距离不平衡的最佳运输方式

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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.