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# On Sparsity Inducing Regularization Methods for Machine Learning

Abstract : 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 $\omega$ 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 $\omega$ 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-00855984
Contributor : Puneet Kumar Dokania Connect in order to contact the contributor
Submitted on : Friday, August 30, 2013 - 11:49:32 AM
Last modification on : Friday, January 21, 2022 - 3:01:24 AM

### Identifiers

• HAL Id : hal-00855984, version 1
• ARXIV : 1303.6086

### Citation

Andreas Argyriou, Luca Baldassarre, Charles A. Micchelli, Massimiliano Pontil. On Sparsity Inducing Regularization Methods for Machine Learning. 2013. ⟨hal-00855984⟩

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