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Volume 2 (2006) Article 8 pp. 147-172
On Learning Random DNF Formulas Under the Uniform Distribution
Received: March 21, 2006
Published: September 19, 2006
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Keywords: computational learning theory, uniform-distribution learning, PAC learning, DNF formulas, monotone DNF
ACM Classification: I.2.6, F.2.2, G.1.2, G.3
AMS Classification: 68Q32, 68W20, 68W25, 60C05

Abstract: [Plain Text Version]

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 $\gamma>0$, a random $t$-term monotone DNF for any $t = O(n^{2-\gamma})$. We also define a model of random non-monotone DNF and give an efficient algorithm which with high probability can learn a random $t$-term DNF for any $t=O(n^{3/2 - \gamma})$. These are the first known algorithms that can learn a broad class of polynomial-size DNF in a reasonable average-case model of learning from random examples.