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Technological advances have led to a proliferation of structured big datathat have matrix-valued covariates. We are specifically motivated to buildpredictive models for multi-subject neuroimaging data based on each subject'sbrain imaging scans. This is an ultra-high-dimensional problem that consists ofa matrix of covariates (brain locations by time points) for each subject; fewmethods currently exist to fit supervised models directly to this tensor data.We propose a novel modeling and algorithmic strategy to apply generalizedlinear models (GLMs) to this massive tensor data in which one set of variablesis associated with locations. Our method begins by fitting GLMs to eachlocation separately, and then builds an ensemble by blending information acrosslocations through regularization with what we term an aggregating penalty. Ourso called, Local-Aggregate Model, can be fit in a completely distributed mannerover the locations using an Alternating Direction Method of Multipliers (ADMM)strategy, and thus greatly reduces the computational burden. Furthermore, wepropose to select the appropriate model through a novel sequence of fasteralgorithmic solutions that is similar to regularization paths. We willdemonstrate both the computational and predictive modeling advantages of ourmethods via simulations and an EEG classification problem.

Local-Aggregate Modeling for Big-Data via Distributed Optimization: Applications to Neuroimaging