Abstract

We study gene interaction networks using Gaussian graphical models that represent the underlying graph structure of conditional dependence between random variables determined by their partial correlation or precision matrix. In a high dimensional setting, the precision matrix is estimated using penalized likelihood by adding a penalization term which controls the amount of sparsity in the precision matrix and totally characterizes the complexity and structure of the graph. The most commonly used penalization term is the L1 norm of the precision matrix scaled by the regularization parameter which determines the tradeoff between sparsity of the graph and fit to the data. We propose several procedures to select the regularization parameter in the estimation of graphical models that focus on recovering reliably the appropriate network characteristic of the graph, and discuss their Bayesian interpretation. Performance is illustrated on simulated data as well as on colon tumor gene expression data. This work is extended to reconstructing a differential network between two paired groups of samples.    

This is joint work with with Adria Caballe Mestres (University of Edinburgh and Biomathematics and Statistics Scotland) and Claus Mayer (Biomathematics and Statistics Scotland).