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My question is two fold,

  • Is there any general understanding of what makes a function class have high Rademacher complexity? (Sudakov minoration would say that one sufficient condition for a class of functions to have a high Rademacher complexity is if it has high packing number in the corresponding pseudo-metric. So one can also ask as to if we know of properties of a function class which will lead it to have a large packing number.)

  • A possibly commonly occurring situation is that over some domain X, we explicitly know of a function $g^* : X \rightarrow \mathbb{R}$ and we look at the $\epsilon-$ball around $g^*$ inside some larger function space $F$. Is there anything known about conditions when is such an epsilon ball around a specific function of high Rademacher complexity?

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  • $\begingroup$ Why is this getting a negative vote!? Is anything wrong with the question? $\endgroup$ – gradstudent Mar 12 at 21:46

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