A focused information criterion for graphical models

A new method for model selection for Gaussian Bayesian networks and Markov networks, with extensions towards ancestral graphs, is constructed to have good mean squared error properties. The method is based on the focused information criterion, and offers the possibility of fitting individual-tailored models. The focus of the research, that is, the purpose of the model, directs the selection. It is shown that using the focused information criterion leads to a graph with small mean squared error. The low mean squared error ensures accurate estimation using a graphical model; here estimation rather than explanation is the main objective. Two situations that commonly occur in practice are treated: a data-driven estimation of a graphical model and the improvement of an already pre-specified feasible model. The search algorithms are illustrated by means of data examples and are compared with existing methods in a simulation study.