Network induced large correlation matrix estimation

TL;DR

This paper introduces a two-step method for estimating large correlation matrices in biomedical data by detecting latent graph structures and using them to improve regularization, reducing errors and revealing biological networks.

Contribution

The paper presents a novel approach that combines graph topology detection with correlation matrix regularization, enhancing accuracy and interpretability in high-dimensional biomedical data.

Findings

Graph-guided thresholding reduces false positives and negatives.

Detected latent structures reveal underlying biological networks.

Method improves correlation estimation accuracy.

Abstract

The correlation matrix of massive biomedical data (e.g. gene expression or neuroimaging data) often exhibits a complex and organized, yet latent graph topological structure. We propose a two step procedure that first detects the latent graph topology with parsimony from the sample correlation matrix and then regularizes the correlation matrix by leveraging the detected graph topological information. We show that the graph topological information guided thresholding can reduce false positive and false negative rates simultaneously because it allows edges to borrow strengths from each other precisely. Several examples illustrate that the parsimoniously detected latent graph topological structures may reveal underlying biological networks and guide correlation matrix estimation.