Modeling Disease Progression Flexibly with Nonlinear Disease Structure via Multi-task Learning

Alzheimer's Disease (AD) is the most common dementia characterized by loss of brain function. Multi-tasking learning methods have been widely used to predict cognitive performance and select important imaging biomarkers in AD research. The temporal smoothness assumption, prevalent for modeling AD progression, means the difference between cognitive scores at two consecutive time points is relatively small. However, it's not appropriate due to the presence of sample disturbance and the effectiveness of drug therapy. In addition, many multi-task learning methods select discriminative feature subset from MRI features, assuming that correlations between tasks are consistent, which ignores the complex intrinsic correlation structure of tasks. In this paper, we present a multi-task learning framework which utilizes generalized fused Lasso and generalized group Lasso (GFGGL for abbreviation) to model the disease progression with the complex intrinsic nonlinear structures of disease. The proposed framework is more flexible to utilize the inherent nonlinear relation of AD than existing methods for the reason of we represent the intrinsic structure as three correlation matrices which are functions of super parameters. The framework involves (1) two nonlinear structures of disease progression and (2) one nonlinear structure among tasks. An efficient optimization method is designed for the difficult optimization problem due to the presence of three nonsmooth penalties. Extensive experimental results using dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI) demonstrate the effectiveness of the proposed method.