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Pattern classification problems in the context of neuroimaging data are often highly underdetermined. For example, a typical fMRI data might have 100,000 features (voxels) with only a few hunderds of training examples (stimuli presented). In this case, we have infinitely solutions and we have to pick one solution that is more "reasonable" out of infinitely many of them. To tackle this issue of underdeterminacy while fitting whole brain models (i.e. without pre-defining ROI), we tend to use sparse methods, such as the Logistic LASSO, which will be the main focus of this tutorial.
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Picture from: The Elements of Statistical Learning