False Discovery Rate Control for Sparse Correlation Matrix

Abstract

Abstract Motivation 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 minimisation via cross-validation. Results In this study, we propose a novel alternative thresholding strategy based on an empirical Bayes framework that controls the false discovery rate (FDR) among non-zero 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 non zero correlations. By formulating the construction of 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 minimisation of Frobenius norm. Availability and Implementation The relevant R package called scfdr is available from github.com/ariefgusnanto/scfdr