A Novel Robust Precision Matrix Estimation for High-Dimensional Microbiome Data

A key task in microbiome data analysis is to estimate the dependence pattern among different microbial taxa. However, microbiome datasets from the real world impose a great challenge on standard correlation analysis due to various factors, such as sum-to-one constraint and heavy tails. To handle this challenge, this paper proposes a robust precision matrix estimation by assuming that the log-basis random vector follows a class of continuous elliptical distributions. The proposed Kendall's tau statistics based estimation procedure enjoys several desirable properties. Theoretically, we derive the convergence rate of the proposed estimator under the spectral norm. The sign consistency is also established via a thresholding step. Computationally, the proposed estimator can be computed by linear programming. So we can employ it to large-scale datasets. Empirically, simulation studies and an application to a mouse skin microbiome dataset are conducted to corroborate the superiority of the proposed method.