Communications of the ACM
Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
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
Computational limitations on learning from examples
Journal of the ACM (JACM)
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Learning DNF under the uniform distribution in quasi-polynomial time
COLT '90 Proceedings of the third annual workshop on Computational learning theory
When won't membership queries help?
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
On deterministic approximation of DNF
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Learning decision trees using the Fourier spectrum
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Learning monotone ku DNF formulas on product distributions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Learning 2u DNF formulas and ku decision trees
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Exact learning of read-twice DNF formulas (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Learning the Fourier spectrum of probabilistic lists and trees
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Cryptographic lower bounds for learnability of Boolean functions on the uniform distribution
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Cryptographic hardness of distribution-specific learning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Amplification of weak learning under the uniform distribution
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
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
On the Fourier spectrum of monotone functions
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Learning using group representations (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
On the Fourier spectrum of monotone functions
Journal of the ACM (JACM)
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
A Simulated Annealing-Based Learning Algorithm for Boolean DNF
AI '99 Proceedings of the 12th Australian Joint Conference on Artificial Intelligence: Advanced Topics in Artificial Intelligence
Generalized Graph Colorability and Compressibility of Boolean Formulae
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
CRYPTO '93 Proceedings of the 13th Annual International Cryptology Conference on Advances in Cryptology
Learning Sub-classes of Monotone DNF on the Uniform Distribution
ALT '98 Proceedings of the 9th International Conference on Algorithmic Learning Theory
More efficient PAC-learning of DNF with membership queries under the uniform distribution
Journal of Computer and System Sciences
A lower bound for agnostically learning disjunctions
COLT'07 Proceedings of the 20th annual conference on Learning theory
Learning DNF by statistical and proper distance queries under the uniform distribution
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
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We show that a DNF with terms of size at most d can be approximated by a function with at most dO(d log 1/&egr;))non zero Fourier coefficients such that the expected error squared, with respect to the uniform distribution, is at most &egr;. This property is used to derive a learning algorithm for DNF, under the uniform distribution.The learning algorithm uses queries and learns, with respect to the uniform distribution, a DNF with terms of size at most d in time polynomial in n and dO(d log 1/egr;). The interesting implications are for the case when &egr; is constant. In this case our algorithm learns a DNF with a polynomial number of terms in time nO(log log n), and a DNF with terms of size at most O(log n/log log n) in polynomial time.