Can anyone shed some light on how the VC Dimension affects the sample complexity bounds of infinite hypothesis classes with real-valued outputs in PAC learning, or how to calculate the sample complexity bounds of said classes with some other measure of the class's 'complexity'?
I'm studying machine learning theory, particularly the PAC model, and been having trouble finding some definitive upper and lower bounds on the sample complexity for real-valued hypothesis classes, like those given for binary classification classes with the 0-1 Loss. I know the PAC model and VC Dimension have been generalised to real-valued functions, but at this stage the actual work of Vapnik is a bit impenetrable to me. Still, the VC Dimension still seems like a very intuitive measure to use when determining number of samples you're likely to need to learn a given class; too few samples given the complexity and your learner can't have a clear enough picture of the underlying distribution, and too many and those extra samples aren't really going to improve the learner's capability to learn.
The literature that's out there seems very disjointed, I understand the field is constantly in motion so I'm trying to catch up, without necessarily knowing where 'up' is.