Conditional Kernel Covariance and Correlation  

条件核协方差与相关性

作　　者：BAI Qianxue SHI Yuke YANG Qing LI Qizhai 白千雪;石宇珂;杨青;李启寨(中国科学院数学与系统科学研究院系统科学研究所,北京,100190;中国科学院大学数学科学学院,北京100049;中南民族大学数学与统计学学院,湖北武汉430074)

机构地区：[1]Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences [2]School of Mathematical Sciences,University of Chinese Academy of Sciences [3]School of Mathematics and Statistics,South-Central Minzu University

出　　处：《数学进展》2024年第6期1158-1172,共15页Advances in Mathematics（China）

基　　金：partially supported by Knowledge Innovation Program of Hubei Province(No.2019CFB810);partially supported by NSFC(No.12325110);the CAS Project for Young Scientists in Basic Research(No.YSBR-034)。

摘　　要：The conditional kernel correlation is proposed to measure the relationship between two random variables under covariates for multivariate data.Relying on the framework of reproducing kernel Hilbert spaces,we give the definitions of the conditional kernel covariance and conditional kernel correlation.We also provide their respective sample estimators and give the asymptotic properties,which help us construct a conditional independence test.According to the numerical results,the proposed test is more effective compared to the existing one under the considered scenarios.A real data is further analyzed to illustrate the efficacy of the proposed method.本文提出了条件核相关性来衡量多元数据中存在协变量的条件下两个随机变量之间的关系.基于再生核希尔伯特空间,我们给出了条件核协方差和条件核相关性的定义.同时,我们还给出了它们的样本估计以及渐近性质,并基于此构造了条件独立性检验.根据数值结果,在文中所示的情况下,本文所提出的检验与现有检验相比更有效.通过对实际数据的进一步分析,验证了所提出方法的有效性.

关 键 词：conditional kernel correlation reproducing kernel Hilbert space conditional independence test 

分 类 号：O212.4[理学—概率论与数理统计]