Reviews: Testing for Differences in Gaussian Graphical Models: Applications to Brain Connectivity

The goal of improving testing for differences between graphs is clearly relevant to neuroimaging and other application domains. While the specifics are somewhat incremental, I think this is a great idea, and reasonably well executed. Major issues: * Please explain specifically which gradients are used to get from (4) to (5). This derivation seems incorrect if one takes separate derivatives with respect to \beta_1 and \beta_2. How do you end up with a sum of terms (and not two separate terms)?