The human cortex encodes information in complex networks that can be anatomically dispersed and variable in their microstructure across individuals. Using simulations with neural network models, we show that contemporary statistical methods for functional brain imaging—including univariate contrast, searchlight multivariate pattern classification, and whole-brain decoding with L1 or L2 regularization—each have critical and complementary blind-spots under these conditions. We then introduce the sparse-overlapping-sets (SOS) LASSO: a whole-brain multivariate approach that exploits structured sparsity to find network-distributed information and show in simulation that it captures the advantages of other approaches while avoiding their limitations. When applied to fMRI data to find neural responses that discriminate visually presented faces from other visual stimuli, each method yields a different result, but existing approaches all support the canonical view that face perception engages localized areas in pos...