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Trying to explain the idea of VC to some of my colleagues I've discovered quite an intuitive way of laying out the basic idea. Without going through lots of math and notation as I've done in my other answer. Imagine a following game between two players $\alpha$ and $\beta$ : First, player $\alpha$ plots $d=4$ points on a piece of paper. She may place the ...


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Shattered set. First we need a concept of a shattered set. I'll work from a shattered set example in Wikipedia adjusting it to your notation. The statement that $\mathcal{H}$ shatters $C$ means that for every subset $A \subset C$ there is a set $B\in\mathcal{H}$ such that $B$ "separates" $A$ from $C \backslash A$. Writing this formally: $$\text{...


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