  Determining functional brain connectivity is crucial to understanding the
brain and neural differences underlying disorders such as autism. Recent
studies have used Gaussian graphical models to learn brain connectivity via
statistical dependencies across brain regions from neuroimaging. However,
previous studies often fail to properly incorporate priors tailored to
neuroscience, such as preferring shorter connections. To remedy this problem,
the paper here introduces a novel, weighted-$\ell_1$, multi-task graphical
model (W-SIMULE). This model elegantly incorporates a flexible prior, along
with a parallelizable formulation. Additionally, W-SIMULE extends the
often-used Gaussian assumption, leading to considerable performance increases.
Here, applications to fMRI data show that W-SIMULE succeeds in determining
functional connectivity in terms of (1) log-likelihood, (2) finding edges that
differentiate groups, and (3) classifying different groups based on their
connectivity, achieving 58.6\% accuracy on the ABIDE dataset. Having
established W-SIMULE's effectiveness, it links four key areas to autism, all of
which are consistent with the literature. Due to its elegant domain adaptivity,
W-SIMULE can be readily applied to various data types to effectively estimate
connectivity.
