Learning a function from noisy samples at a finite sparse set of points

In learning theory the goal is to reconstruct a function defined on some (typically high dimensional) domain ΩΩ, when only noisy values of this function at a sparse, discrete subset ω⊂Ωω⊂Ω are available.In this work we use Koksma–Hlawka type estimates to obtain deterministic bounds on the so-called generalization error. The resulting estimates show that the generalization error tends to zero when the noise in the measurements tends to zero and the number of sampling points tends to infinity sufficiently fast.