A Kernel-based Test of Independence for Cluster-correlated DataDownload PDF

May 21, 2021 (edited Nov 09, 2021)NeurIPS 2021 PosterReaders: Everyone
  • Keywords: multivariate analysis, kernel methods, independence test, correlated data
  • TL;DR: We propose a novel kernel-based test to evaluate the dependence between two multivariate variables based on cluster-correlated data.
  • Abstract: The Hilbert-Schmidt Independence Criterion (HSIC) is a powerful kernel-based statistic for assessing the generalized dependence between two multivariate variables. However, independence testing based on the HSIC is not directly possible for cluster-correlated data. Such a correlation pattern among the observations arises in many practical situations, e.g., family-based and longitudinal data, and requires proper accommodation. Therefore, we propose a novel HSIC-based independence test to evaluate the dependence between two multivariate variables based on cluster-correlated data. Using the previously proposed empirical HSIC as our test statistic, we derive its asymptotic distribution under the null hypothesis of independence between the two variables but in the presence of sample correlation. Based on both simulation studies and real data analysis, we show that, with clustered data, our approach effectively controls type I error and has a higher statistical power than competing methods.
  • Supplementary Material: pdf
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  • Code: https://github.com/pearl-liu/HSIC_cl
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