An Efficient Projection for L1 Infinity Regularization

author: Ariadna Quattoni, Universitat Politècnica de Catalunya
published: Aug. 26, 2009,   recorded: June 2009,   views: 7244


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In recent years the L1,Infinity norm has been proposed for joint regularization. In essence, this type of regularization aims at extending the L1 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 L1,Infinity regularized problems. The main challenge in developing such a method resides on being able to compute efficient projections to the L1,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 L1,Infinity leads to better performance than both L2 and L1 regularization and that it is is effective in discovering jointly sparse solutions.

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