Interpretable whole-brain prediction analysis with GraphNet.

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 Graph-constrained Elastic-Net (GraphNet), a fast, whole-brain regression and classification method developed for spatially and temporally correlated data that automatically yields interpretable coefficient maps (Grosenick et al., 2009b). GraphNet methods yield sparse but structured solutions by combining structured graph constraints (based on knowledge about coefficient smoothness or connectivity) with a global sparsity-inducing prior that automatically selects important variables. Because GraphNet methods can efficiently fit regression or classification models to whole-brain, multiple time-point data sets and enhance classification accuracy relative to volume-of-interest (VOI) approaches, they eliminate the need for inherently biased VOI analyses and allow whole-brain fitting without the multiple comparison problems that plague mass univariate and roaming VOI ("searchlight") methods. As fMRI data are unlikely to be normally distributed, 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 (Knutson et al., 2007), these efficient whole-brain methods significantly improved classification accuracy over previously reported VOI-based analyses on the same data (Grosenick et al., 2008; Knutson et al., 2007) while discovering task-related regions not documented in the original VOI approach. Critically, GraphNet estimates fit to the Knutson et al. (2007) data generalize well to out-of-sample data collected more than three years later on the same task but with different subjects and stimuli (Karmarkar et al., submitted for publication). 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.