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Gaussian graphical models represent the underlying graph structure ofconditional dependence between random variables which can be determined usingtheir partial correlation or precision matrix. In a high-dimensional setting,the precision matrix is estimated using penalized likelihood by adding apenalization term which controls the amount of sparsity in the precision matrixand totally characterizes the complexity and structure of the graph. The mostcommonly used penalization term is the L1 norm of the precision matrix scaledby the regularization parameter which determines the trade-off between sparsityof the graph and fit to the data. In this paper we propose several proceduresto select the regularization parameter in the estimation of graphical modelsthat focus on recovering reliably the appropriate network structure of thegraph. We conduct an extensive simulation study to show that the proposedmethods produce useful results for different network topologies. The approachesare also applied in a high-dimensional real case study of gene expression datawith the aim to discover the genes relevant to colon cancer. Using this data,we find graph structures which are verified to display significant biologicalgene associations.

Selection of the Regularization Parameter in Graphical Models using Network Characteristics