I begin the post trying to say that i don't know if this post is in compliance to community rules, so pardon me for any abuse.
I studied back at the university statistical learning theory. I studied PAC learning, VC Dimension, Uniform convergence etc etc. Recently i watched this talk with Vapnik https://www.youtube.com/watch?v=STFcvzoxVw4&t=1346s in which he claims that deep learning is essentially a "bla bla interpretation" and also claims that 'every problem can be solved with statistical learning theory'.
I'm very confused about this. I can't see how I can apply statistical learning theory on real problems. Let's suppose I'm facing a new dataset with a clear task of binary classification, with many features and lots of training data. How am I supposed to check for example, if a hypothesis class H is PAC learnable, or in other words if it has a finite VC dimension? Don't take my example too literally, I just want to know if someone can point me out to an article,blog or some kind of answer that clearly shows how we can use this theorems and results in a real analysis.