Network induced large correlation matrix estimation

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.