Statistics Seminar: STA 290
Thursday, March 8th, 2012 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments: 3.30pm, MSB 1147 (Colloquium Room)
Speaker: Lexin Li (Dept. Statistics, North Carolina State University)
Title: Tensor Regression with Applications in Neuroimaging Data Analysis
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 high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this talk, we propose a new family 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. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data. We will also briefly discuss a number of extensions of tensor regression.