论文标题
地球搬家的相关性
The Earth Mover's Correlation
论文作者
论文摘要
自从19世纪末引入了皮尔逊的相关性以来，文献中已经出现了许多依赖措施。最近，我们提出了四个简单的公理，用于依赖于希尔伯特空间中值的随机变量。我们表明距离相关满足所有这些公理。我们仍然需要一种新的依赖度量，因为现有措施要么在一般度量空间（不是希尔伯特空间）不起作用，要么不满足我们的四个简单公理。本文引入的地球移动器的相关性适用于一般度量空间，并满足我们的四个公理（其中两个以较弱的形式）。
Since Pearson's correlation was introduced at the end of the 19th century many dependence measures have appeared in the literature. Recently we have suggested four simple axioms for dependence measures of random variables that take values in Hilbert spaces. We showed that distance correlation satisfies all these axioms. We still need a new measure of dependence because existing measures either do not work in general metric spaces (that are not Hilbert spaces) or they do not satisfy our four simple axioms. The earth mover's correlation introduced in this paper applies in general metric spaces and satisfies our four axioms (two of them in a weaker form).
