论文标题
Azadkia-Chatterjee的相关系数适应了数据
Azadkia-Chatterjee's correlation coefficient adapts to manifold data
论文作者
论文摘要
在他们的开创性工作中，Azadkia和Chatterjee（2021）启动了基于图的方法，用于测量可变依赖强度。通过吸引最近的邻居图，他们为Rényi问题提供了优雅的解决方案（Rényi，1959年）。他们的想法后来在Deb等人中发展。 （2020）那里的作者证明，有趣的是，Azadkia和Chatterjee的相关系数可以自动适应数据的歧管结构。本文在计算独立性下的统计限制方差方面进一步进一步研究，并表明它仅取决于歧管维度。
In their seminal work, Azadkia and Chatterjee (2021) initiated graph-based methods for measuring variable dependence strength. By appealing to nearest neighbor graphs, they gave an elegant solution to a problem of Rényi (Rényi, 1959). Their idea was later developed in Deb et al. (2020) and the authors there proved that, quite interestingly, Azadkia and Chatterjee's correlation coefficient can automatically adapt to the manifold structure of the data. This paper furthers their study in terms of calculating the statistic's limiting variance under independence and showing that it only depends on the manifold dimension.
