Tensor Regression, Regularization, and Imaging Analysis

• Activity Number: 275
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Lexin Li*+ and Hua Zhou and Hongtu Zhu
• Companies: North Carolina State University and North Carolina State University and University of North Carolina at Chapel Hill
• Keywords: Dimension reduction ; Magnetic resonance imaging ; Regularization ; Tensor regression

Abstract

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are compromised for analysis of those high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this talk, I will discuss a new class of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. Regularization, both hard thresholding and soft thresholding types, will be carefully examined. The new methods aim to address a family of neuroimaging problems, including using brain images to diagnose neurodegenerative disorders, to predict onset of neuropsychiatric diseases, and to identify disease relevant brain regions or activity patterns.