Functional neuroimaging measures how the brain responds to complex stimuli. However, sample sizes are modest, noise is substantial, and stimuli are high dimensional. Hence, direct estimates are inherently imprecise and call for regularization. We compare a suite of approaches which regularize via shrinkage: ridge regression, the elastic net (a generalization of ridge regression and the lasso), and a hierarchical Bayesian model based on small area estimation (SAE). We contrast regularization with spatial smoothing and combinations of smoothing and shrinkage. All methods are tested on functional magnetic resonance imaging (fMRI) data from multiple subjects participating in two different experiments related to reading, for both predicting neural response to stimuli and decoding stimuli from responses. Interestingly, when the regularization parameters are chosen by cross-validation independently for every voxel, low/high regularization is chosen in voxels where the classification accuracy is high/low, indicating that the regularization intensity is a good tool for identification of relevant voxels for the cognitive task. Surprisingly, all the regularization methods work about equally well, suggesting that beating basic smoothing and shrinkage will take not only clever methods, but also careful modeling.
"Regularized brain reading with shrinkage and smoothing." Ann. Appl. Stat. 9 (4) 1997 - 2022, December 2015. https://doi.org/10.1214/15-AOAS837