Wavelet interpolation networks.
Christophe P. Bernard, Stéphane Mallat, Jean-Jacques E. Slotine · 1998
. We describe a new approach to real time learning of unknown functions based on an interpolating wavelet estimation. We choose a subfamily of a wavelet basis relying on nested hierarchical allocation and update in real time our estimate of the unknown function. Such an interpolation process can be used for real time applications like neural network adaptive control, where learning an unknown function very fast is critical. 1. Introduction Our purpose is to approximate an unknown function f : R n ! R from scattered samples (x ø ; y ø = f(x ø )) ø=1:::t , where ffl we have little a priori knowledge on the unknown function f : it lives in some infinite dimensional smooth function space. ffl the function approximation process is performed iteratively: each new measure on the function (x t ; f(x t )) is used to compute a new estimate f t as an update of a previous estimate f t\\Gamma1 . ffl the above update computations and the data storage should be efficient, to fit in a real time l...