Sparse Covariance Matrix Estimation for Compositional Data via a Composition-Adjusted Thresholding

• Activity Number: 510
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Yuanpei Cao*+
• Companies: University of Pennsylvania
• Keywords: sparse ; thresholding ; rate of convergence ; compositional data ; covariance estimation

Abstract

Compositional data are observed in many scientific studies, including human microbiome studies, where only the composition of the bacterial taxa is observed. These data are in a simplex space and therefore the traditional covariance estimation methods cannot be applied directly to analyze such data. In this paper, we introduce a Composition-Adjusted Thresholding (COAT) method to estimate the high dimensional covariance matrix for compositional data under the assumption that the base covariance matrix is sparse. COAT involves a rank-two matrix projection and adaptive thresholding in the complement of the projection space. COAT estimator is adaptive to the variability of individual component and it has strong theoretical properties and carries almost no computational burden. We obtain an explicit convergence rate in the operator norm, which shows the tradeoff between the sparsity of the true model, the dimension and sample size. Simulation results show that COAT estimator outperforms the naive Pearson estimator and estimate of covariance matrix based on log-transformation. We finally present analysis of human gut microbiome data to understand the dependency structure.