Sparse Multi-Response Tensor Regression for Alzheimer's Disease Study with Multivariate Clinical Assessments

Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disorder that has recently seen serious increase in the number of affected subjects. In the last decade, neuroimaging has been shown to be a useful tool to understand AD and its prodromal stage, amnestic mild cognitive impairment (MCI). The majority of AD/MCI studies have focused on disease diagnosis, by formulating the problem as classification with a binary outcome of AD/MCI or healthy controls. There have recently emerged studies that associate image scans with continuous clinical scores that are expected to contain richer information than a binary outcome. However, very few studies aim at modeling multiple clinical scores simultaneously, even though it is commonly conceived that multivariate outcomes provide correlated and complementary information about the disease pathology. In this article, we propose a sparse multi-response tensor regression method to model multiple outcomes jointly as well as to model multiple voxels of an image jointly. The proposed method is particularly useful to both infer clinical scores and thus disease diagnosis, and to identify brain subregions that are highly relevant to the disease outcomes. We conducted experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, and showed that the proposed method enhances the performance and clearly outperforms the competing solutions.