Multi-Task Learning in Square Integrable Space

Several kernel based methods for multi-task learning have been proposed, which leverage relations among tasks as regularization to enhance the overall learning accuracies. These methods assume that the tasks share the same kernel, which could limit their applications because in practice different tasks may need different kernels. The main challenge of introducing multiple kernels into multiple tasks is that models from different Reproducing Kernel Hilbert Spaces (RKHSs) are not comparable, making it difficult to exploit relations among tasks. This paper addresses the challenge by formalizing the problem in the Square Integrable Space (SIS). Specially, it proposes a kernel based method which makes use of a regularization term defined in the SIS to represent task relations. We prove a new representer theorem for the proposed approach in SIS. We further derive a practical method for solving the learning problem and conduct consistency analysis of the method. We discuss the relations between our method and an existing method. We also give an SVM based implementation of our method for multi-label classification. Experiments on two real-world data sets show that the proposed method performs better than the existing method.