Penalized estimation of sparse concentration matrices based on prior knowledge with applications to placenta elemental data

Identifying patterns of association or dependency among high-dimensional biological datasets with sparse precision matrices remains a challenge. In this paper, we introduce a weighted sparse Gaussian graphical model that can incorporate prior knowledge to infer the structure of the network of trace element concentrations, including essential elements as well as toxic metals and metaloids measured in the human placentas. We present the weighted L1 penalized regularization procedure for estimating the sparse precision matrix in the setting of Gaussian graphical models. First, we use simulation models to demonstrate that the proposed method yields a better estimate of the precision matrix than the procedures that fail to account for the prior knowledge of the network structure. Then, we apply this method to estimate sparse element concentration matrices of placental biopsies from the New Hampshire Birth Cohort Study. The chemical architecture for elements is complex; thus, the method proposed herein was applied to infer the dependency structures of the elements using prior knowledge of their biological roles.