Joint Estimation of Sparse Networks with application to Paired Gene Expression data

We consider a method to jointly estimate sparse precision matrices and their underlying graph structures using dependent high-dimensional datasets. We present a penalized maximum likelihood estimator which encourages both sparsity and similarity in the estimated precision matrices where tuning parameters are automatically selected by controlling the expected number of false positive edges. We also incorporate an extra step to remove edges which represent an overestimation of triangular motifs. We conduct a simulation study to show that the proposed methodology presents consistent results for different combinations of sample size and dimension. Then, we apply the suggested approaches to a high-dimensional real case study of gene expression data with samples in two medical conditions, healthy and colon cancer tissues, to estimate a common network of genes as well as the differentially connected genes that are important to the disease. We find denser graph structures for healthy samples than for tumor samples, with groups of genes interacting together in the shape of clusters.