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
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
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
Exact learning Boolean functions via the monotone theory
Information and Computation
On the Fourier spectrum of monotone functions
Journal of the ACM (JACM)
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
Machine Learning
Machine Learning
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Approximate lineage for probabilistic databases
Proceedings of the VLDB Endowment
Application of a generalization of russo's formula to learning from multiple random oracles
Combinatorics, Probability and Computing
On evolvability: the swapping algorithm, product distributions, and covariance
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
Learning juntas in the presence of noise
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
On the learnability of shuffle ideals
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
Learnability of DNF with representation-specific queries
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
A composition theorem for the fourier entropy-influence conjecture
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We show that the class of monotone 2O(√logn)-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. We also show that various classes of small constant-depth circuits which compute monotone functions are PAC learnable in polynomial time under the uniform distribution. All of our results extend to learning under any constant-bounded product distribution.