We kindly invite you to the talk "Individual Function Approximation and Cross-validation " by Felix Bartel. Wednesday, Feb. 9, 3:00pm Vienna Time.

Join either online – contact to get an invite link – or in SR7, Oskar-Morgenstern-Platz 1, Vienna

In this talk we present joint work with Daniel Potts and Ralf Hielscher on scattered data approximation for individual functions (Monte Carlo setting). We show error bounds for the least squares method in the $L_2$-norm which hold with high probability. These bounds are also applicable for noisy samples. The error behavior poses the question of model selection. Here, we utilize leave-one-out cross-validaiton. We show, that the cross-validation score can be computed in a fast manner in this context. Further, we give error guarantees which validate cross-validation in model selection.