3
$\begingroup$

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.

$\endgroup$

1 Answer 1

2
$\begingroup$

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/

$\endgroup$
5
  • $\begingroup$ Are there any more examples? $\endgroup$
    – Meni
    Apr 1, 2017 at 19:43
  • 1
    $\begingroup$ The $\gamma$-shattering dimension of hyperplanes on a ball of radius $R$ is $(R/\gamma)^2$. $\endgroup$
    – Aryeh
    Apr 1, 2017 at 20:20
  • $\begingroup$ Care for a proof or s link to one? :-) $\endgroup$
    – Meni
    Apr 1, 2017 at 20:42
  • $\begingroup$ citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.6950 $\endgroup$
    – Aryeh
    Apr 1, 2017 at 22:20
  • 1
    $\begingroup$ See Theorem 1.6 $\endgroup$
    – Aryeh
    Apr 1, 2017 at 22:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.