Title: Estimating organized large covariance matrix with $l_0$ penalty
Authors: Shuo Chen - University of Maryland, School of Medicine (United States) [presenting]
Abstract: Interactions between features of high-dimensional biomedical data often exhibit complex and organized, yet latent, network topological structures. Estimating the organized large covariance matrix of these high-dimensional biomedical data while preserving and recognizing the latent network topology are challenging. A new $l_0$ shrinkage large covariance procedure is proposed that first detects latent network topological structures by implementing new penalized optimization and then regularizes the covariance matrix by leveraging the detected network topological information. The network topology guided regularization can reduce false positive and false negative rates simultaneously because it allows edges to borrow strengths from each other precisely. We provide applications to several large biomedical data examples including proteomics, genomics, and metabolomics data and demonstrate that organized latent network topological structures widely exist in high-dimensional biomedical data across platforms. In these applications, our methods show robust performance and scalability for identifying network structures. We also extend this method to detect network structures beyond the community structure.