Technical Report Details
| Date |
9-6-2009 |
| Number |
DISI-TR-09-01 |
| Title |
An Iterative Projection Procedure to Solve Sparsity Based Regularization |
| Authors |
Sofia Mosci, Lorenzo Rosasco, Matteo Santoro, Alessandro Verri, SIlvia Villa |
| Bibtex Entry |
@techreport{morosa09,
author={Mosci, S. and Rosasco, L. and Santoro, M. and Verri, A. and Villa, S. |
| E-mail |
mosci@disi.unige.it |
| Link |
ftp://ftp.disi.unige.it/person/MosciS/PAPERS/sparse_fenchel_TR.pdf |
| Abstract |
In this paper we propose a general framework to characterize and solve
the optimization problems underlying a large class of sparsity based regularization
algorithms. More precisely, we study the minimization of learning functionals
that are sums of a differentiable data term and a convex non differentiable penalty.
These latter penalties have recently become popular since they allow to enforce various kinds of
sparsity in the solution. Leveraging on the theory of Fenchel
duality and subdifferential calculus, we derive explicit optimality conditions for the regularized
solution and propose an extremely simple, yet general, iterative projection algorithm
whose convergence to the optimal solution can be proved. The generality of the framework
is illustrated, considering several examples of regularization schemes
including l_1 regularization (and several variants), multiple kernel learning and multi-task learning.
Finally some distinctive features of the proposed framework are studied by empirical investigation. |
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