A Kernel Approach to Multi-Task Learning with Task-Specific Kernels

• Published in: Journal of computer science and technology 2012-11, Vol.27 (6), p.1289-1301
• Main Author: 武威 李航 胡云华 金榕
• Format: Article
• Language: English
• Subjects: Analysis; Artificial Intelligence; Classification; Computer Science; Consistency; Data Structures and Information Theory; Datasets; Experiments; Hilbert space; Information Systems Applications (incl.Internet); Kernels; Learning; Mathematical analysis; Methods; Regular Paper; Regularization; Software Engineering; Studies; Support vector machines; Tasks; Theory of Computation; Vectors (mathematics); 内核; 再生核希尔伯特空间; 多任务; 学习问题; 支持向量机; 正则化; 积空间; 表现定理
• ISSN: 1000-9000; 1860-4749
• DOI: 10.1007/s11390-012-1305-1

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 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 relationship between our method and an existing method. We also give an SVM （support vector machine）- based implementation of our method for multi-label classification. Experiments on an artificial example and two real-world datasets show that the proposed method performs better than the existing method.