On Sparsity Inducing Regularization Methods for Machine Learning

03/25/2013

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by   Andreas Argyriou, et al.

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During the past years there has been an explosion of interest in learning methods based on sparsity regularization. In this paper, we discuss a general class of such methods, in which the regularizer can be expressed as the composition of a convex function ω with a linear function. This setting includes several methods such the group Lasso, the Fused Lasso, multi-task learning and many more. We present a general approach for solving regularization problems of this kind, under the assumption that the proximity operator of the function ω is available. Furthermore, we comment on the application of this approach to support vector machines, a technique pioneered by the groundbreaking work of Vladimir Vapnik.