It doesn't change what I said. Every class of functions that has the universal approximation property can be used to "learn" from data. This is what statistical

It doesn't change what I said. Every class of functions that has the universal approximation property can be used to "learn" from data. This is what statistical learning is about. You can use trees, random forests, piecewise linear functions, multidimensional adaptive regression splines (MARS), multidimensional fourier series or wavelets, radial basis functions, the list goes on and on. And people have been using all these methods with success. The idea that the universal approximation theorem is something special about neural networks is completely wrong. Deep learning is valuable because it represents a class of functions closed under composition. That allows it to discover features at different scales. You can in principle add composability to other classes of functions. You would end up with deep splines, for example. Or deep radial basis functions, or deep wavelets. And people have tried those, but it just didn't take off. It was probably the advantage of the first mover. Deep NN's turned out to be useful, people built a large ecosystem for them, and then other deep things (like deep splines or wavelets) just did not show a significant advantage. Yet.