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Abstract and Applied Analysis
Volume 2013, Article ID 715275, 7 pages
Research Article

Least Square Regularized Regression for Multitask Learning

1Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China
2Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100091, China
3Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong

Received 11 October 2013; Accepted 13 November 2013

Academic Editor: Yiming Ying

Copyright © 2013 Yong-Li Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The study of multitask learning algorithms is one of very important issues. This paper proposes a least-square regularized regression algorithm for multi-task learning with hypothesis space being the union of a sequence of Hilbert spaces. The algorithm consists of two steps of selecting the optimal Hilbert space and searching for the optimal function. We assume that the distributions of different tasks are related to a set of transformations under which any Hilbert space in the hypothesis space is norm invariant. We prove that under the above assumption the optimal prediction function of every task is in the same Hilbert space. Based on this result, a pivotal error decomposition is founded, which can use samples of related tasks to bound excess error of the target task. We obtain an upper bound for the sample error of related tasks, and based on this bound, potential faster learning rates are obtained compared to single-task learning algorithms.