What do you mean? what do you think statistical modelling is? I am very confused by your stance. The aim of the function approximation is to maximize the like

What do you mean? what do you think statistical modelling is? I am very confused by your stance. The aim of the function approximation is to maximize the likelihood of the observed data (this is standard statistical modelling), using machine learning (e.g., stochastic gradient decent) on a class of universal function approximators is a standard approach to fitting such a model. What do you think statistical modelling involves?