Learning pseudo-Boolean k-DNF and Submodular Functions

  title={Learning pseudo-Boolean k-DNF and Submodular Functions},
  author={Sofya Raskhodnikova and Grigory Yaroslavtsev},
We prove that any submodular function f : {0, 1}n → {0, 1, ..., k} can be represented as a pseudoBoolean2k-DNF formula. Pseudo-Boolean DNFs are a natural generaliza tion of DNF representation for functions with integer range. Each term in such a formula has an associated integral constant. We show that an analog of Håstad’s switching lemma holds for pseudo -Bo leank-DNFs if all constants associated with the terms of the formula are bounded. This allows us to generalize Mansour’s PAC-learning… CONTINUE READING
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