False discovery rate control for sparse correlation matrix

In genomic data analysis, high-dimensional correlation matrices pose challenges in interpreting complex relationships among genomic features, particularly due to overfitting. Traditional approaches generate sparse correlation matrices by setting correlations below a predetermined threshold to zero, with the threshold typically determined through Frobenius norm minimization via cross-validation.

In this study, we propose a novel alternative thresholding strategy based on an empirical Bayes framework that controls the false discovery rate among nonzero correlations. This method offers two key advantages: first, it is compatible with any correlation measure and, second, it provides an estimation of the expected false positives among nonzero correlations. By formulating the construction of a sparse correlation matrix as both an estimation and an inference problem, our approach enhances interpretability and demonstrates greater sensitivity in retaining true biological correlations than threshold selection based on the minimization of Frobenius norm.

The relevant R package called scfdr is available from github.com/ariefgusnanto/scfdr.