Communications of the ACM
Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
On the learnability of Boolean formulae
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
A guided tour of Chernoff bounds
Information Processing Letters
Learning DNF under the uniform distribution in quasi-polynomial time
COLT '90 Proceedings of the third annual workshop on Computational learning theory
Learning monotone ku DNF formulas on product distributions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Improved learning of AC0 functions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
The complexity of finite functions
Handbook of theoretical computer science (vol. A)
A technique for upper bounding the spectral norm with applications to learning
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The complexity of learning formulas and decision trees that have restricted reads
The complexity of learning formulas and decision trees that have restricted reads
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
On using the Fourier transform to learn Disjoint DNF
Information Processing Letters
Learning monotone log-term DNF formulas
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
On learning monotone DNF formulae under uniform distributions
Information and Computation
Weakly learning DNF and characterizing statistical query learning using Fourier analysis
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
An O(nlog log n) learning algorithm for DNF under the uniform distribution
Journal of Computer and System Sciences
Fast learning of k-term DNF formulas with queries
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Exact learning Boolean functions via the monotone theory
Information and Computation
On the Fourier spectrum of monotone functions
Journal of the ACM (JACM)
A simple algorithm for learning O (log n)-term DNF
Information Processing Letters
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
More efficient PAC-learning of DNF with membership queries under the uniform distribution
COLT '99 Proceedings of the twelfth annual conference on Computational learning theory
Learning Sub-classes of Monotone DNF on the Uniform Distribution
ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On the applications of multiplicity automata in learning
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Learning DNF from random walks
Journal of Computer and System Sciences - Special issue: Learning theory 2003
On learning random DNF formulas under the uniform distribution
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
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We show that the class of monotone 2O(√ n)-term DNF formulae can be PAC learned in polynomial time under the uniform distribution from random examples only. This is an exponential improvement over the best previous polynomial-time algorithms in this model, which could learn monotone o(log2 n)-term DNF, and is the first efficient algorithm for monotone (log n)ω(1)-term DNF in any nontrivial model of learning from random examples. We also show that various classes of small constant-depth circuits which compute monotone functions on few input variables are PAC learnable in polynomial time under the uniform distribution. All of our results extend to learning under any constantbounded product distribution.