High-Dimensional Robust Covariance Matrix Estimation for Compositional Microbiome Data

• Activity Number: 123 - New Challenges and Opportunities in Nonparametric Statistics
• Type: Topic Contributed
• Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Arun Srinivasan* and Lingzhou Xue and Xiang Zhan
• Companies: Pennsylvania State University and Penn State University and National Institute of Statistical Sciences and Penn State University
• Keywords: Covariance Matrix Estimation; Microbiome; Robust; High-dimensional

Abstract

A fundamental problem in microbiome is studying the covariance or interaction among microbial taxa, especially how the relationship varies under different conditions. However, microbiome data is littered with many statistical challenges such as high-dimensionality, a compositional structure, and the heavy-tailed taxa distributions. Existing methods for covariance matrix estimation of microbiome data do not take into account possible heavy-tails and outliers. We propose a new robust estimation procedure to construct a sparse estimation of the covariance structure of high-dimensional compositional microbiome data. This proposed method firstly constructs a robust estimator of the covariance structure of compositional data and then employs an l1-penalization based thresholding method to induce sparsity. We demonstrate the effectiveness of our method through numerical studies and illustrate its usefulness by applying our method to an inflammatory bowel disease-microbiome data analyzing the differences in the microbial community of individuals with and without antibiotics use.