VC generalization bound extended to other types of target functions In Y. S. Abu-Mostafa's book &quot;Learning from Data&quot;, he mentions on page 55 after deriving the VC generalization bound for a binary target function that &quot;it can be extended to other types of target functions&quot;. I have looked online for quite a bit but it's really not clear to me how that should work. I'm particularly interested in continuous target functions, where hypothesis $h \in \mathcal{H}$ maps input space $\mathcal{X}$ to $\mathbb{R}^N$, rather than classifications. But I don't see how shattering could be adapted for these target functions.
Pseudo dimension and fat shattering dimension are (some of the) analogue of VC dimension in the regression setting. See https://ttic.uchicago.edu/~tewari/lectures/lecture15.pdf (section 3)