In many fields one needs to build predictive models for a set of related machine learning tasks, such as information retrieval, computer vision and biomedical informatics. Traditionally these tasks are treated independently and the inference is done separately for each task, which ignores important connections among the tasks. Multi-task learning aims at simultaneously building models for all tasks in order to improve the generalization performance, leveraging inherent relatedness of these tasks. In this thesis, I firstly propose a clustered multi-task learning (CMTL) formulation, which simultaneously learns task models and performs task clustering. I provide theoretical analysis to establish the equivalence between the CMTL formulation and the alternating structure optimization, which learns a shared low-dimensional hypothesis space for different tasks. Then I present two real-world biomedical informatics applications which can benefit from multi-task learning. In the first application, I study the disease progression problem and present multi-task learning formulations for disease progression. In the formulations, the prediction at each point is a regression task and multiple tasks at different time points are learned simultaneously, leveraging the temporal smoothness among the tasks. The proposed formulations have been tested extensively on predicting the progression of the Alzheimer's disease, and experimental results demonstrate the effectiveness of the proposed models. In the second application, I present a novel data-driven framework for densifying the electronic medical records (EMR) to overcome the sparsity problem in predictive modeling using EMR. The densification of each patient is a learning task, and the proposed algorithm simultaneously densify all patients. As such, the densification of one patient leverages useful information from other patients.