George A. Anastassiou and Dimitra Kouloumpou
Approximation of Multiple Time Separating Random Functions by Neural Networks Revisited
Neural Parallel and Scientific Computations 32 (2024) 37-48
https://doi.org/10.46719/NPSC2024.32.03
ABSTRACT.
Here we study the multivariate quantitative approximation of multiple time separating random functions over a RN, N ∈ N, by the normalized bell and squashing type multivariate neural network operators. Activation functions here are of compact support. These approximations are derived by establishing Jackson type multivariate inequalities involving the multivariate modulus of continuity of the engaged random function or its high order partial derivatives. The approximations are pointwise and with respect to the LP norm. The feed-forward neural networks are with one hidden layer. We finish with a variety of interesting applications.
AMS (MOS) Subject Classification. 26A15, 41A17, 41A25, 60H25.
Keywords and Phrases: Multiple time separating random functions, multivariate neural network approximation, multivariate modulus of continuity, activation functions of compact support, squashing functions.