Low-rank, Orthogonally Decomposable Tensor Regression

Oregon Convention Center 

Multi-dimensional tensor data have gained increasing attention in the recent years. We consider the problem of fitting a generalized linear model with a three-dimensional image covariate, such as one obtained by functional magnetic resonance imaging (fMRI). Many of the classical penalized regression techniques do not account for the spatial structure in imaging data. We assume the parameter tensor is orthogonally decomposable, enabling us to penalize the tensor singular values and avoid a priori specification of the rank. Under this assumption, we additionally propose to penalize internal variation of the parameter tensor. Our approach provides an effective method to reduce the dimensionality and control piecewise smoothness of imaging data. Effectiveness of our method is demonstrated on synthetic data and real MRI imaging data.

Low-rank approximation

Tensor regression

Nuclear norm

Internal variation 

Korean International Statistical Society