Learning Graphical Models With Hubs.

We consider the problem of learning a high-dimensional graphical model in which there are a few nodes that are to many other nodes. Many authors have studied the use of an penalty in order to learn a sparse graph in the high-dimensional setting. However, the penalty implicitly assumes that each edge is equally likely and independent of all other edges.

Node-Based Learning of Multiple Gaussian Graphical Models.

We consider the problem of estimating high-dimensional Gaussian graphical models corresponding to a single set of variables under several distinct conditions. This problem is motivated by the task of recovering transcriptional regulatory networks on the basis of gene expression data containing heterogeneous samples, such as different disease states, multiple species, or different developmental stages. We assume that most aspects of the conditional dependence networks are shared, but that there are some structured differences between them.