It is often the case that the VC-dimension of a hypothesis class equals (or can be bounded above by) the number of parameters one needs to set in order to define each hypothesis in the class.

For instance, if $H$ is the class of axis aligned rectangles in $R^d$, then $VCdim(H) = 2d$ , which is equal to the number of parameters used to define a rectangle in $R^d$.

How do you understand such a phenomenon?


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