Sparse model-based network inference using Gaussian graphical models

We consider the problem of estimating a sparse dynamic Gaussian graphical model with L1 penalized maximum likelihood of structured precision matrix. The structure can consist of specific time dynamics, known presence or absence of links in the graphical model or equality constraints on the parameters. The model is defined on the basis of partial correlations, which results in a specific class precision matrices. A priori L1 penalized maximum likelihood estimation in this class is extremely difficult, because of the above mentioned constraints, the computational complexity of the L1 constraint on the side of the usual positive-definite constraint. The implementation is non-trivial, but we show that the com- putation can be done effectively by taking advantage of an efficient maximum determinant algorithm (SDPT3) developed in convex optimization. For selecting the tuning parameter, we compare several selection criteria and argue that the traditional AIC and BIC should not expect to work. We compare our method with related methods, such as glasso (Friedman et al. 2007).