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8 votes
2 answers
1k views

VC dimension, fat-shattering dimension, and other complexity measures, of a class BV functions

I wish to show that a function which is "essentially constant" (defined shortly) can't be a good classifier (machine learning). For this i need to estimate the "complexity" of such a class of ...
dohmatob's user avatar
  • 6,853
2 votes
1 answer
1k views

Packing number of Lipschitz functions

For some $L>0$ say ${\cal L}$ is the space of all $L-$Lipschitz functions mapping $(X,\rho) \rightarrow [0,1]$ where $(X,\rho)$ is a metric space. For any $\alpha >0$ do we know of a ...
gradstudent's user avatar
  • 2,246
2 votes
0 answers
292 views

Covering/Bracketing number of monotone functions on $\mathbb{R}$ with uniformly bounded derivatives

I am interested in the $\| \cdot \|_{\infty}$-norm bracketing number or covering number of some collection of distribution functions on $\mathbb{R}$. Let $\mathcal{F}$ consist of all distribution ...
masala's user avatar
  • 93