title: Local-aggregate modeling for big data via distributed optimization: Applications to neuroimaging.
abstract: Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging scans. This is an ultra-high-dimensional problem that consists of a matrix of covariates (brain locations by time points) for each subject; few methods currently exist to fit supervised models directly to this tensor data. We propose a novel modeling and algorithmic strategy to apply generalized linear models (GLMs) to this massive tensor data in which one set of variables is associated with locations. Our method begins by fitting GLMs to each location separately, and then builds an ensemble by blending information across locations through regularization with what we term an aggregating penalty. Our so called, Local-Aggregate Model, can be fit in a completely distributed manner over the locations using an Alternating Direction Method of Multipliers (ADMM) strategy, and thus greatly reduces the computational burden. Furthermore, we propose to select the appropriate model through a novel sequence of faster algorithmic solutions that is similar to regularization paths. We will demonstrate both the computational and predictive modeling advantages of our methods via simulations and an EEG classification problem.
authors: Department of Statistics, Rice University.
authors: Yue
authors: Y
authors: Hu
authors: Dobelman Family Junior Chair Departments of Statistics and Electrical & Computer Engineering, Rice University, Department of Pediatrics-Neurology, Baylor College of Medicine, Jan and Dan Duncan Neurological Research Institute, Texas Children's Hospital.
authors: Genevera I
authors: GI
authors: Allen
mesh_terms: D000465:Algorithms; D001699:Biometry / Q000379:methods; D003198:Computer Simulation; D004569:Electroencephalography / Q000706:statistics & numerical data; D006801:Humans; D016014:Linear Models; D000069550:Machine Learning / Q000706:statistics & numerical data; D059906:Neuroimaging / Q000706:statistics & numerical data*; D012044:Regression Analysis
keywords: ADMM; Big data; Ensemble learning; Generalized linear models; Multi-subject neuroimaging; Parallel computing; Regularization paths