  Multivariate machine learning methods are increasingly used to analyze
neuroimaging data, often replacing more traditional "mass univariate"
techniques that fit data one voxel at a time. In the functional magnetic
resonance imaging (fMRI) literature, this has led to broad application of
"off-the-shelf" classification and regression methods. These generic approaches
allow investigators to use ready-made algorithms to accurately decode
perceptual, cognitive, or behavioral states from distributed patterns of neural
activity. However, when applied to correlated whole-brain fMRI data these
methods suffer from coefficient instability, are sensitive to outliers, and
yield dense solutions that are hard to interpret without arbitrary
thresholding. Here, we develop variants of the the Graph-constrained Elastic
Net (GraphNet), ..., we (1) extend GraphNet to include robust loss functions
that confer insensitivity to outliers, (2) equip them with "adaptive" penalties
that asymptotically guarantee correct variable selection, and (3) develop a
novel sparse structured Support Vector GraphNet classifier (SVGN). When applied
to previously published data, these efficient whole-brain methods significantly
improved classification accuracy over previously reported VOI-based analyses on
the same data while discovering task-related regions not documented in the
original VOI approach. Critically, GraphNet estimates generalize well to
out-of-sample data collected more than three years later on the same task but
with different subjects and stimuli. By enabling robust and efficient selection
of important voxels from whole-brain data taken over multiple time points
(>100,000 "features"), these methods enable data-driven selection of brain
areas that accurately predict single-trial behavior within and across
individuals.
