Learning rates of neural network estimators via the new FNNs operators

In this paper, estimation of a regression function with independent and identically distributed random variables is investigated. The regression estimators are defined by minimization of empirical least-square regularized algorithm over a class of functions, which are defined by the feed forward neural networks (FNNs). In order to derive the learning rates of these FNNs regression function estimators, the new FNNs operators are constructed via modified sigmoidal functions. Vapnik-Chervonenkis dimension (V-C dimension) of the class of FNNs functions is also discussed. In addition, the direct approximation theorem by the neural network operators in L_ρx² with Borel probability measure ρ is established.