What are some good examples for analysis of a class's Fat-Shattering dimension?

By (Alon et al) I know that the Fat-Shattering Dimension characterizes the learnability of real-valued function classes but I didn't find any proper examples of function class with a proof for a bound on the Fat-Shattering Dimension of the class.


For $L$-Lipschitz functions on a metric space $(X,\rho)$ with $\epsilon$-packing number $M(\epsilon)$, the $\gamma$-shattering dimension is $M(2\gamma/L)$, as proved here: http://ieeexplore.ieee.org/document/6867374/

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  • $\begingroup$ Are there any more examples? $\endgroup$ – Meni Apr 1 '17 at 19:43
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    $\begingroup$ The $\gamma$-shattering dimension of hyperplanes on a ball of radius $R$ is $(R/\gamma)^2$. $\endgroup$ – Aryeh Apr 1 '17 at 20:20
  • $\begingroup$ Care for a proof or s link to one? :-) $\endgroup$ – Meni Apr 1 '17 at 20:42
  • $\begingroup$ citeseerx.ist.psu.edu/viewdoc/summary?doi= $\endgroup$ – Aryeh Apr 1 '17 at 22:20
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    $\begingroup$ See Theorem 1.6 $\endgroup$ – Aryeh Apr 1 '17 at 22:20

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