Corpus ID: 6496642

Representation, Approximation and Learning of Submodular Functions Using Low-rank Decision Trees

@inproceedings{Feldman2013RepresentationAA,
  title={Representation, Approximation and Learning of Submodular Functions Using Low-rank Decision Trees},
  author={Vitaly Feldman and Pravesh Kothari and Jan Vondr{\'a}k},
  booktitle={COLT},
  year={2013}
}
  • Vitaly Feldman, Pravesh Kothari, Jan Vondrák
  • Published in COLT 2013
  • Computer Science, Mathematics
  • We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube $\{0,1\}^n$. Our main result is the following structural theorem: any submodular function is $\epsilon$-close in $\ell_2$ to a real-valued decision tree (DT) of depth $O(1/\epsilon^2)$. This immediately implies that any submodular function is $\epsilon$-close to a function of at most $2^{O(1/\epsilon^2)}$ variables and has a spectral $\ell_1$ norm of… CONTINUE READING

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    A tree of rank2k over |J | variables has size of at most|J |2k (Ehrenfeucht and Haussler

    • 1989