Learning Random Dnf Over the Uniform Distribution.
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Learning Random Dnf Over the Uniform Distribution.

Learning Random Dnf Over the Uniform Distribution.


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This thesis presents a new result for exactly learning the average monotone clog(n)-DNF formulae and average clog( n)-DNF formulae from random examples drawn from the uniform distribution. Learning DNF with a DNF hypothesis has often been called one of the most important problems in computational learning theory. Valiant, who founded the field of computational learning theory, stated in his seminal paper [Val84], "Such expressions appear particularly easy for humans to comprehend. Hence we expect that any practical learning system would have to allow for them." Yet learning DNF by DNF has proved elusive; learning k-term DNF by k-term DNF is NP-hard even with membership queries and under the uniform distribution [Fel06]. In this thesis we prove that despite the fact that this class is NP-hard to learn, the average member of this class where the terms are of a fixed size is easy to exactly learn---even when only provided with random examples from the uniform distribution. We show that randomly generated monotone clog( n)-DNF formulae and randomly generated clog( n)-DNF formulas can be exactly learned in probabilistic polynomial time over the uniform distribution. Our notion of randomly generated is with respect to a uniform distribution. To prove this we identify the class of well behaved clog( n)-DNF formulae, and the prominent property of terms in a DNF-formula. We show that almost every monotone DNF formula and almost every DNF formula is well-behaved, and is composed entirely of prominent terms. We prove that there exists a probabilistic Turing machine that exactly learns the prominent terms of well behaved clog( n)-DNF formula. This thesis presents the first algorithm for exactly learning a large class of DNF formulae when only given access to labeled examples drawn from the uniform distribution. A key contribution of this thesis is to show that there exists a simple test that finds subsets of terms in most k-DNF formulae (monotone or non-monotone).


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Product Details
  • ISBN-13: 9781243470096
  • Publisher: Proquest, Umi Dissertation Publishing
  • Publisher Imprint: Proquest, Umi Dissertation Publishing
  • Height: 246 mm
  • Weight: 136 gr
  • ISBN-10: 1243470097
  • Publisher Date: 01 Sep 2011
  • Binding: Paperback
  • Spine Width: 4 mm
  • Width: 189 mm


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Learning Random Dnf Over the Uniform Distribution.
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