Symmetric Tensor Regression with Applications in Neuroimaging Data Analysis

• Activity Number: 253
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Weixin Cai* and Lexin Li
• Companies: University of California at Berkeley and University of California at Berkeley
• Keywords: Brain imaging ; Dimension reduction ; Generalized linear model ; Magnetic Resonance Imaging ; Tensor regression ; Functional connectivity

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 proving insufficient for analysis of these high­throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we consider regression with symmetric tensor covariates. Such data occur naturally in many applications. In the connectivity analysis in neuroimaging studies, neuroscientists partition brain into functional regions and study the relationship between the trait(s) and the connectivity among regions. The proposed method allows trait to be either continuous, binary (disease or not), count, or multivariate. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. This method will also require asymptotic results to be established and fast, highly scalable estimation algorithm implemented. Effectiveness of the new methods is demonstrated on both synthetic and real imaging data