Communications of the ACM
Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
Learning decision trees from random examples needed for learning
Information and Computation
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Boosting a weak learning algorithm by majority
COLT '90 Proceedings of the third annual workshop on Computational learning theory
A polynomial time algorithm that learns two hidden unit nets
Neural Computation
Rank-r decision trees are a subclass of r-decision lists
Information Processing Letters
Cryptographic hardness of distribution-specific learning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Threshold circuits of bounded depth
Journal of Computer and System Sciences
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
On the computational power of depth 2 circuits with threshold and modulo gates
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
PP is closed under intersection
Selected papers of the 23rd annual ACM symposium on Theory of computing
When do extra majority gates help?: polylog(N) majority gates are equivalent to one
Computational Complexity - Special issue on circuit complexity
On the Fourier spectrum of monotone functions
Journal of the ACM (JACM)
A subexponential exact learning algorithm for DNF using equivalence queries
Information Processing Letters
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
MadaBoost: A Modification of AdaBoost
COLT '00 Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
Learning DNF by Approximating Inclusion-Exclusion Formulae
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
A Random Sampling based Algorithm for Learning the Intersection of Half-spaces
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Efficient algorithms in computational learning theory
Efficient algorithms in computational learning theory
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Learning intersections and thresholds of halfspaces
Journal of Computer and System Sciences - Special issue on FOCS 2002
Learning functions of k relevant variables
Journal of Computer and System Sciences - Special issue: STOC 2003
Agnostically Learning Halfspaces
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Learning DNF from random walks
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Learning a circuit by injecting values
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Separating Models of Learning from Correlated and Uncorrelated Data
The Journal of Machine Learning Research
The complexity of properly learning simple concept classes
Journal of Computer and System Sciences
Learning unions of ω(1)-dimensional rectangles
Theoretical Computer Science
Learning a circuit by injecting values
Journal of Computer and System Sciences
Efficient learning algorithms yield circuit lower bounds
Journal of Computer and System Sciences
Learning large-alphabet and analog circuits with value injection queries
COLT'07 Proceedings of the 20th annual conference on Learning theory
Bounding the average sensitivity and noise sensitivity of polynomial threshold functions
Proceedings of the forty-second ACM symposium on Theory of computing
Learning and lower bounds for AC0 with threshold gates
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Discrete Applied Mathematics
Learning unions of ω(1)-dimensional rectangles
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Private data release via learning thresholds
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Learning DNF by statistical and proper distance queries under the uniform distribution
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
Efficient learning algorithms yield circuit lower bounds
COLT'06 Proceedings of the 19th annual conference on Learning Theory
On PAC learning algorithms for rich boolean function classes
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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
Separating models of learning from correlated and uncorrelated data
COLT'05 Proceedings of the 18th annual conference on Learning Theory
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We give an algorithm to learn constant-depth polynomial-size circuits augmented with majority gates under the uniform distribution using random examples only. For circuits which contain a polylogarithmic number of majority gates the algorithm runs in quasipolynomial time. This is the first algorithm for learning a more expressive circuit class than the class AC0 of constant-depth polynomial-size circuits, a class which was shown to be learnable in quasipolynomial time by Linial, Mansour and Nisan in 1989. Our approach combines an extension of some of the Fourier analysis from Linial et al. with hypothesis boosting. We also show that under a standard cryptographic assumption our algorithm is essentially optimal with respect to both running time and expressiveness (number of majority gates) of the circuits being learned.