Vapnik–Chervonenkis dimension

just storing tabs here for now:

• https://en.wikipedia.org/wiki/VC_dimension
• https://www.quora.com/Explain-VC-dimension-and-shattering-in-lucid-Way
• https://www.google.com/search?q=VC%20dimension
• https://en.wikipedia.org/wiki/Shattered_set
• https://math.stackexchange.com/questions/96655/how-to-calculate-vapnik-chervonenkis-dimension
• baum's What is thought contains a discussion

I think there's three different "views" of the VC dimension:

• in terms of sets/powersets and shattering
• in terms of fitting parameters for a function
• adversarial/game: to show the VC dimension is at least n: you choose n points, the adversary chooses the labels, you must find a hypothesis from the hypothesis class that separates the labels cleanly

questions:

• does this work with more than two labels? (with the power sets view, obviously there's only yes/no classifications. but with the other two views, you can generalize to more labels; does doing this yield anything useful?)
• in the adversarial perspective, why do you get to pick the points? (this is a question about which definition is most useful.) is there a name for the thing where you can separate all points and all labels?
• where does the hypothesis class come from? it seems like "lines", "circles", "convex sets" are some examples used.