Kernel Basis Pursuit
Vincent Guigue, Alain Rakotomamonjy and Stéphane Canu
Revue d'Intelligence Artificielle
Estimating a non-uniformly sampled function from a set of learning points is a clas-
sical 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
1 -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 compu-
tation 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 aim at proposing a
fast parameter-free method to estimate non-uniform-sampled functions.