Multi-task learning via structured regularization: formulations, algorithms, and applications

Multi-task learning (MTL) aims to improve the generalization performance (of the resulting classifiers) by learning multiple related tasks simultaneously. Specifically, MTL exploits the intrinsic task relatedness, based on which the informative domain knowledge from each task can be shared across multiple tasks and thus facilitate the individual task learning. It is particularly desirable to share the domain knowledge (among the tasks) when there are a number of related tasks but only limited training data is available for each task. Modeling the relationship of multiple tasks is critical to the generalization performance of the MTL algorithms. In this dissertation, I propose a series of MTL approaches which assume that multiple tasks are intrinsically related via a shared low-dimensional feature space. The proposed MTL approaches are developed to deal with different scenarios and settings; they are respectively formulated as mathematical optimization problems of minimizing the empirical loss regularized by different structures. For all proposed MTL formulations, I develop the associated optimization algorithms to find their globally optimal solution efficiently. I also conduct theoretical analysis for certain MTL approaches by deriving the globally optimal solution recovery condition and the performance bound. To demonstrate the practical performance, I apply the proposed MTL approaches on different real-world applications: (1) Automated annotation of the Drosophila gene expression pattern images; (2) Categorization of the Yahoo web pages. Our experimental results demonstrate the efficiency and effectiveness of the proposed algorithms.