On learning random DNF formulas under the uniform distribution

Authors:
Jeffrey C. Jackson;Rocco A. Servedio
Affiliations:
Dept. of Math. and Computer Science, Duquesne University, Pittsburgh, PA;Dept. of Computer Science, Columbia University, New York, NY
Venue:
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Year:
2005

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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 γ0, a random t-term monotone DNF for any t = O(n2−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(n3/2−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.