[LAMPS] A kernel based approximation for constrained optimal smoothing problem

Résumé

If the constrained optimal smoothing problem is posed in a Reproducing Kernel Hilbert Space, there is a new way of approaching it by defining a sequence of finite dimensional Reproducing Kernel Hilbert Spaces and a particular manner to discretize the problem. We present this method of approximation and prove its convergence to the exact solution. This problem can be reformulated as a Bayesian estimation problem involving a Gaussian process related to the kernel of the RKHS. Our approximation corresponds to its Maximum A Posteriori. We propose an error bounds for the convergence of a piecewise linear approximation of the constrained optimal smoothing problem which depends of the grid size, the regularity of the kernel, and the distance from the kernel interpolant of the approximation to the set of constraints.

Intervenant