基于成分调整的协方差估计
Large Covariance Estimation for Compositional Data via Composition-Adjusted Thresholding
摘要：
高维组成数据在诸如宏基因组数据分析等许多应用中自然出现。观测数据是一个高维的单纯形，传统的统计方法往往无法产生合理的结果，由于单位和约束。本文研究了高维成分数据的协方差估计问题，并在基协方差阵稀疏的假设下，提出了一种成分调整阈值（COAT）方法。我们的方法是基于一个分解有关的组成协方差的基础协方差，这是近似可识别的维数趋于无穷大。由此产生的过程可以被视为阈值的样本中心的对数比协方差矩阵，因此是可扩展的大协方差阵。我们严格的协方差参数的可识别性的特点，得到的频谱范数下的收敛速度，并提供理论保证支持恢复。模拟研究表明，COAT估计优于一些天真的阈值估计，忽略了独特的组成数据的功能。我们将所提出的方法应用于微生物组数据集的分析，以了解人类肠道中细菌类群之间的依赖结构。
英文摘要：
High-dimensional compositional data arise naturally in many applications such as metagenomic data analysis. The observed data lie in a high-dimensional simplex, and conventional statistical methods often fail to produce sensible results due to the unit-sum constraint. In this article, we address the problem of covariance estimation for high-dimensional compositional data, and introduce a composition-adjusted thresholding (COAT) method under the assumption that the basis covariance matrix is sparse. Our method is based on a decomposition relating the compositional covariance to the basis covariance, which is approximately identifiable as the dimensionality tends to infinity. The resulting procedure can be viewed as thresholding the sample centered log-ratio covariance matrix and hence is scalable for large covariance matrices. We rigorously characterize the identifiability of the covariance parameters, derive rates of convergence under the spectral norm, and provide theoretical guarantees on support recovery. Simulation studies demonstrate that the COAT estimator outperforms some naive thresholding estimators that ignore the unique features of compositional data. We apply the proposed method to the analysis of a microbiome dataset in order to understand the dependence structure among bacterial taxa in the human gut.
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