Abstract
Despite the advance in medical research, there are still some diseases that cannot be cured after certain level of severity. For instance, Alzheimer’s disease (AD), arguably the best known neurodegenerative disease, attracts significant attention because of its irreversible disease progression. Enormous capital and efforts have been invested into AD research for the pursuit of better prediction on its progression. While there are multiple ways to solve disease progression problem, multitask learning is the predominant strategy due to its strength of sharing partial information across time points to compensate the effect of insufficient data. In this paper, we extend algorithms for disease progression prediction from equipping one-dimensional proximal constraints to two-dimensional ones along with an assumption on the smoothness of features across time points. Our model achieves significant improvement in AD progression prediction on the basis of multitask learning model comparing with the previous works. Beside the empirical improvement, in this paper we provide theoretical analysis to show that the proposed two-dimensional proximal constraints maintains the feasibility of the decomposition procedure on derived optimization. We not only solve L2 norm models optimally, but also provide an approximation solution for models with L1 norm. Our implementation extends MALSAR library package, which is used specifically for multitask learning, and is available online.
Keywords
Two-dimensional Proximal Constraints, Multitask Learning, Irreversible Disease, Alzheimer’s Disease, Disease Progression Prediction, Fused Lasso, Group Lasso