Integrating Additional Knowledge Into Estimation of Graphical Models

Abstract: In applications of graphical models, we typically have more information than just the samples themselves. A prime example is the estimation of brain connectivity networks based on fMRI data, where in addition to the samples themselves, the spatial positions of the measurements are readily available. With particular regard for this application, we are thus interested in ways to incorporate additional knowledge most effectively into graph estimation. Our approach to this is to make neighborhood selection receptive to additional knowledge by strengthening the role of the tuning parameters. We demonstrate that this concept (i) can improve reproducibility, (ii) is computationally convenient and efficient, and (iii) carries a lucid Bayesian interpretation. We specifically show that the approach provides effective estimations of brain connectivity graphs from fMRI data. However, providing a general scheme for the inclusion of additional knowledge, our concept is expected to have applications in a wide range of domains.