Profile networks for precision medicine

We propose a class of profile graphical models to model the effect of an external factor on the dependence structure of a multivariate set of variables. The main aim is to provide a joint representation based on a single graph of the probability distribution of a multivariate random vector given different levels of an external factor. In particular, we explore the marginal dependence structure by using the subclass of bi-directed profile graphical models and we show that the selected graphical model is compatible with a two block regression graph. An application is discussed based on protein networks in various subtypes of acute myeloid leukemia.