Consistent learning by composite proximal thresholding

Consistent learning by composite proximal thresholding

Composite proximal bundle method

We consider minimization of nonsmooth functions which can be represented as the composition of a positively homogeneous convex function and a smooth mapping. This is a sufficiently rich class that includes max-functions, largest eigenvalue functions, and norm-1 regularized functions. The bundle method uses an oracle that is able to compute separately the function and subgradient information for...

Thresholding in Learning Theory

Learning Globally Consistent Maps by Relaxation

Proximal Thresholding Algorithm for Minimization over Orthonormal Bases

The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties, providing in particular several characterizations of such thresholders. W...