B0384
Title: Evading the curse of dimensionality in nonparametric regression with deep neural networks
Authors: Sophie Langer - University Twente (Germany) [presenting]
Abstract: In the classical multivariate regression context, it is well-known that any nonparametric method is affected by the so-called curse of dimensionality, meaning that convergence of the estimators slows down as dimension increases. We show how one can evade this phenomenon by using estimators based on deep neural networks and restricting the class of regression functions in a proper sense. In a second result, we consider the case that the predictor variable is concentrated on a manifold and show again that deep neural network estimators achieve a convergence rate independent of dimension.
