Consistency of biological networks inferred from microarray and sequencing data

Penalized estimation of the Gaussian graphical model from data with replicates

Gaussian graphical models are usually estimated from unreplicated data. The data are, however, likely to comprise signal and noise. These two cannot be deconvoluted from unreplicated data. Pragmatically, the noise is then ignored in practice. We point out the consequences of this practice for the reconstruction of the conditional independence graph of the signal. Replicated data allow for the deconvolution of signal and noise and the reconstruction of former's conditional independence graph. Hereto we present a penalized Expectation-Maximization algorithm. The penalty parameter is chosen to maximize the F-fold cross-validated log-likelihood. Sampling schemes of the folds from replicated data are discussed. By simulation we investigate the effect of replicates on the reconstruction of the signal's conditional independence graph. Moreover, we compare the proposed method to several obvious competitors. In an application we use data from oncogenomic studies with replicates to reconstruct the gene-gene interaction networks, operationalized as conditional independence graphs. This yields a realistic portrait of the effect of ignoring other sources but sampling variation. In addition, it bears implications on the reproducibility of inferred gene-gene interaction networks reported in literature.

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.