Kernel Basis Pursuit ## AbstractEstimating 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 L 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.
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