CARE: Large Precision Matrix Estimation for Compositional Data

doi:10.1080/01621459.2024.2335586

CARE: Large Precision Matrix Estimation for Compositional Data

2024-04-29

1

OA

AI

DOI：10.1080/01621459.2024.2335586

Original

Original request for help

Save

Abstract

En 中文

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a large precision matrix. We introduce a precise specification of the compositional precision matrix and relate it to its basis counterpart, which is shown to be asymptotically identifiable under suitable sparsity assumptions. By exploiting this connection, we propose a composition adaptive regularized estimation (CARE) method for estimating the sparse basis precision matrix. We derive rates of convergence for the estimator and provide theoretical guarantees on support recovery and data-driven parameter tuning. Our theory reveals an intriguing tradeoff between identification and estimation, thereby highlighting the blessing of dimensionality in compositional data analysis. In particular, in sufficiently high dimensions, the CARE estimator achieves minimax optimality and performs as well as if the basis were observed. We further discuss how our framework can be extended to handle data containing zeros, including sampling zeros and structural zeros. The advantages of CARE over existing methods are illustrated by simulation studies and an application to inferring microbial ecological networks in the human gut. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Keywords:

Blessing of dimensionality

Graphical modeling

High-dimensional data

Identifiability

Microbiome

CARE: Large Precision Matrix Estimation for Compositional Data

Abstract

Journal

Organization