# 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} }

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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