There is no subject under the name "Statistics and Nonlinear Function Approximation" that describes the algorithms involved in NLP. No subject or concept in the name "Statistics and Nonlinear Function Approximation" that describes the history and codification of breaking down an image into thousands of additional images and then performing the "statistics" - there is much more in ML/AI than what you'd like to call that college.
Neural networks are all "nonlinear function approximation". Last I checked, the state-of-the-art in all the fields you mention is some variation of deep neural network.
Not to be despicable. On the contrary, function approximation is a very rich and deep topic.
