An efficient projection for l1,∞ regularization
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Collins_An efficient.pdf
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Author(s)
Quattoni, Ariadna
Carreras Perez, Xavier
Collins, Michael
Alternative Title
An efficient projection for l [subscript 1],[subscript infinity] regularization
Date Issued
January 2009
Journal
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
Abstract
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.
Subjects
algorithms
design
management
performance
theory
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Attribution-Noncommercial-Share Alike 3.0 Unported
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DOI of Published Version
https://doi.org/10.1145/1553374.1553484
