On Sparsity Inducing Regularization Methods for Machine Learning

During the past few years there has been an explosion of interest in learning methods based on sparsity regularization. In this chapter, 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 as 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.