Rank-based correlation matrix estimation for high dimensional microbiome data

Abstract

In recent years, the progress made in high-throughout sequencing techniques supports the analysis of microbial communities greatly. The fact that real-world microbiome data lie in a high-dimensional simplex makes conventional statistical analysis unreliable owing to the sum-to-one constraint. Motivated by the urgent requirements of directly inferring the dependence pattern and dependence intensity simultaneously among microbial taxa, we address the challenge of correlation matrix estimation for this kind of data. Assuming that the unobserved log-basis random vectors follow the elliptical distribution, a robust method built on the Kendall's tau statistic is developed to estimate the basis generalized correlation matrix. Regardless of the existence of the covariance, the basis generalized correlation matrix is always a reliable measure of dependence structure. Theoretically, we establish the convergence rate of the proposed estimator under the spectral norm. Support recovery is discussed as well. Empirically, simulation studies demonstrate the outstanding numerical performance of our method. We also apply our method to analyse a microbiome dataset from human gut. We provide all the codes at https://github.com/lwfwhunanhero/CRCE.