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Abstract

We study the average-case learnability of DNF formulas in the model of learning from uniformly distributed random examples. We define a natural model of random monotone DNF formulas and give an efficient algorithm which with high probability can learn, for any fixed constant γ> 0, a random t-term monotone DNF for any t = O(n 2 − γ). We also define a model of random nonmonotone DNF and give an efficient algorithm which with high probability can learn a random t-term DNF for any t=O(n 3/2 − γ). These are the first known algorithms that can successfully learn a broad class of polynomial-size DNF in a reasonable average-case model of learning from random examples.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jeffrey C. Jackson
    • 1
  • Rocco A. Servedio
    • 2
  1. 1.Dept. of Math. and Computer ScienceDuquesne UniversityPittsburghUSA
  2. 2.Dept. of Computer ScienceColumbia UniversityNew YorkUSA

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