High-dimensional Graphical Models

Graphical models are now a standard tool in statistics, and
high-dimensional graphical models have been studied extensively. One of the ideas behind graphical models is to break down a high-dimensional problem into several low-dimensional ones. The difficult problem is model selection: one way to do that is to identify the low-dimensional components and see how they fit together. Buhlmann and Meinhausen (2006) were among the first to introduce the local method of neighborhood regression for model selection among graphical Gaussian models. More recent approaches include local l_1 regularized logistic regression for model selection among discrete Ising models, the concept of sparse local separators, and the usage of neighborhood structure. One of the activities of the working group will be review of the current iterature on local methods for structure estimation in high dimension. Another will be the exploration of geometric and topological local methods for the identification of structure in graphical models. Suggestions for other activities are, of course, welcome.