An efficient projection for l1,∞ regularization
Author(s)
Quattoni, Ariadna; Carreras Perez, Xavier; Collins, Michael
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Alternative title
An efficient projection for l [subscript 1],[subscript infinity] regularization
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In recent years the l[subscript 1],[subscript infinity] norm has been proposed for joint regularization. In essence, this type of regularization aims at extending the l[subscript 1] framework for learning sparse models to a setting where the goal is to learn a set of jointly sparse models. In this paper we derive a simple and effective projected gradient method for optimization of l[subscript 1],[subscript infinity] regularized problems. The main challenge in developing such a method resides on being able to compute efficient projections to the l[subscript 1],[subscript infinity] ball. We present an algorithm that works in O(n log n) time and O(n) memory where n is the number of parameters. We test our algorithm in a multi-task image annotation problem. Our results show that l[subscript 1],[subscript infinity] leads to better performance than both l[subscript 2] and l[subscript 1] regularization and that it is is effective in discovering jointly sparse solutions.
Date issued
2009-01Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
Proceedings of the 26th Annual International Conference on Machine Learning
Publisher
Association for Computing Machinery
Citation
Quattoni, Ariadna, Xavier Carreras, Michael Collins, and Trevor Darrell (2009). An efficient projection for l [subscript 1],[subscript infinity] regularization. Proceedings of the 26th Annual International Conference on Machine Learning (New York, N.Y.: ACM): 857-864. © 2009 ACM
Version: Author's final manuscript
ISBN
978-1-60558-516-1
Keywords
algorithms, design, management, performance, theory