Graphical Models

The beginning of this book illustrates that linear regression models can describe the relationships between the genes’ copy numbers and a biomarker. However, those models do not provide information about the relationships among the copy numbers themselves. To describe such relationships, we use a different type of models, called graphical models. We neglect the biomarker and summarize the measured copy numbers in vector-valued observations, where each vector corresponds to a specific subject and each coordinate of these vectors to a specific gene (in the linear regression model, these vectors are the rows of the design matrix). Graphical models then formulate the relationships among the copy numbers as conditional dependence networks among the coordinates of the vector-valued observations. If the observations follow a multivariate Gauss distribution, we speak of Gaussian graphical models. This is the most common class of graphical models and, therefore, the focus of this chapter.