Kernel Basis Pursuit

ABSTRACT. Estimating a non-uniformly sampled function from a set of learning points is a classical regression problem. Kernel methods have been widely used in this context, but every problem leads to two major tasks: optimizing the kernel and setting the fitness-regularization compromise. This article presents a new method to estimate a function from noisy learning points in the context of RKHS (Reproducing Kernel Hilbert Space). We introduce the Kernel Basis Pursuit algorithm, which enables us to build a L1-regularized-multiple-kernel estimator. The general idea is to decompose the function to learn on a sparse-optimal set of spanning functions. Our implementation relies on the Least Absolute Shrinkage and Selection Operator (LASSO) formulation and on the Least Angle Regression Stepwise (LARS) solver. The computation of the full regularization path, through the LARS, will enable us to propose new adaptive criteria to find an optimal fitness-regularization compromise. Finally, we ai...

• Type: Conference
• Year: 2005
• Where: ECML
• Authors: Vincent Guigue, Alain Rakotomamonjy, Stéphane Canu
• Keywords: ECML 2005, Estimer Une Fonction, Kernel Basis Pursuit, Reproducing Kernel Hilbert Space