Estimation of large block structured covariance matrices: Application to "multi-omic" approaches to study seed quality

TL;DR

This paper introduces a new data-driven method for estimating large, block-structured sparse covariance matrices, especially useful in high-dimensional genomics and metabolomics, with practical implementation in an R package and application to seed quality analysis.

Contribution

The paper presents a novel approach for estimating large block-structured covariance matrices that handles unknown permutations and is implemented in an accessible R package.

Findings

The method effectively estimates covariance matrices in high-dimensional settings.

The approach outperforms alternative methods in numerical experiments.

Application to multi-omic data provides insights into seed quality.

Abstract

Motivated by an application in high-throughput genomics and metabolomics, we propose a novel, efficient and fully data-driven approach for estimating large block structured sparse covariance matrices in the case where the number of variables is much larger than the number of samples without limiting ourselves to block diagonal matrices. Our approach consists in approximating such a covariance matrix by the sum of a low-rank sparse matrix and a diagonal matrix. Our methodology also can deal with matrices for which the block structure appears only if the columns and rows are permuted according to an unknown permutation. Our technique is implemented in the R package \texttt{BlockCov} which is available from the Comprehensive R Archive Network (CRAN) and from GitHub. In order to illustrate the statistical and numerical performance of our package some numerical experiments are provided as well as a thorough comparison with alternative methods. Finally, our approach is applied to the use of "multi-omic" approaches for studying seed quality.