Convergence bounds for empirical nonlinear least-squares and applications to tensor recovery

Nom de l'orateur
Philipp Trunschke
Etablissement de l'orateur
Technische Universität Berlin
Date et heure de l'exposé
Lieu de l'exposé

We consider best approximation problems in a nonlinear subset of a Banach space of functions. The norm is assumed to be a generalization of the L2-norm for which only a weighted Monte Carlo estimate can be computed. We establish error bounds for the empirical best approximation error in this general setting and use these bounds to derive a new, sample efficient algorithm for the model set of low-rank tensors. The viability of this algorithm is demonstrated by recovering quantities of interest for a classical random partial differential equation.