Skip to Main content Skip to Navigation
Journal articles

Classification and regression using a constrained convex splitting method

Abstract : This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an $\ell^1$ constraint, a pairwise $\ell^\infty$ constraint, or a pairwise $\ell^1$ constraint. Existing work, such as the Lasso formulation, has focused mainly on Lagrangian penalty approximations, which often require ad hoc or computationally expensive procedures to determine the penalization parameter. We depart from this approach and address the constrained problem directly via a splitting method. The structure of the method is that of the classical gradientprojection algorithm, which alternates a gradient step on the objective and a projection step onto the lower level set modeling the constraint. The novelty of our approach is that the projection step is implemented via an outer approximation scheme in which the constraint set is approximated by a sequence of simple convex sets consisting of the intersection of two half-spaces. Convergence of the iterates generated by the algorithm is established for a general smooth convex minimization problem with inequality constraints. Experiments on both synthetic and biological data show that our method outperforms penalty methods.
Complete list of metadata

Cited literature [35 references]  Display  Hide  Download
Contributor : Michel Barlaud <>
Submitted on : Monday, May 22, 2017 - 12:36:08 PM
Last modification on : Wednesday, October 14, 2020 - 4:22:20 AM
Long-term archiving on: : Wednesday, August 23, 2017 - 3:12:32 PM


Files produced by the author(s)




Michel Barlaud, Wafa Belhajali, Patrick Louis Combettes, Lionel Fillatre. Classification and regression using a constrained convex splitting method. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2017. ⟨hal-01367108⟩



Record views


Files downloads