  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.
