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Exact learning of random DNF over the uniform distribution

Published: 31 May 2009 Publication History

Abstract

We show that randomly generated c log(n)-DNF formula can be learned exactly in probabilistic polynomial time using randomly generated examples. Our notion of randomly generated is with respect to a uniform distribution.
To prove this we extend the concept of well behaved c log(n)-Monotone DNF formulae to c log(n)-DNF formulae, and show that almost every DNF formula is well-behaved, and that there exists a probabilistic polynomial time algorithm that exactly learns all well behaved c log(n)-DNF formula. This is the first algorithm that properly learns (non-monotone) DNF with a polynomial number of terms from random examples alone.

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    cover image ACM Conferences
    STOC '09: Proceedings of the forty-first annual ACM symposium on Theory of computing
    May 2009
    750 pages
    ISBN:9781605585062
    DOI:10.1145/1536414
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    Published: 31 May 2009

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    Author Tags

    1. DNF
    2. learning theory

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    May 31 - June 2, 2009
    MD, Bethesda, USA

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    • (2015)Learning a Random DFA from Uniform Strings and State InformationProceedings of the 26th International Conference on Algorithmic Learning Theory - Volume 935510.1007/978-3-319-24486-0_8(119-133)Online publication date: 4-Oct-2015
    • (2014)Random arithmetic formulas can be reconstructed efficientlyComputational Complexity10.1007/s00037-014-0085-023:2(207-303)Online publication date: 1-Jun-2014
    • (2014)Learning DNF FormulasEncyclopedia of Algorithms10.1007/978-3-642-27848-8_196-2(1-5)Online publication date: 21-Aug-2014
    • (2013)Random Arithmetic Formulas Can Be Reconstructed Efficiently2013 IEEE Conference on Computational Complexity10.1109/CCC.2013.10(1-9)Online publication date: Jun-2013
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    • (2011)On noise-tolerant learning of sparse parities and related problemsProceedings of the 22nd international conference on Algorithmic learning theory10.5555/2050345.2050385(413-424)Online publication date: 5-Oct-2011
    • (2011)Learning random monotone DNFDiscrete Applied Mathematics10.1016/j.dam.2010.08.022159:5(259-271)Online publication date: 1-Mar-2011
    • (2011)On Noise-Tolerant Learning of Sparse Parities and Related ProblemsAlgorithmic Learning Theory10.1007/978-3-642-24412-4_32(413-424)Online publication date: 2011
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