Communications of the ACM
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
A polynomial time algorithm that learns two hidden unit nets
Neural Computation
Surveys in combinatorics, 1993
PP is closed under intersection
Selected papers of the 23rd annual ACM symposium on Theory of computing
Classification by polynomial surfaces
Discrete Applied Mathematics
When do extra majority gates help?: polylog(N) majority gates are equivalent to one
Computational Complexity - Special issue on circuit complexity
Learning an intersection of a constant number of halfspaces over a uniform distribution
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Large margin classification using the perceptron algorithm
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Learning Intersections and Thresholds of Halfspaces
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
New degree bounds for polynomial threshold functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Learning Mixtures of Gaussians
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
An Algorithmic Theory of Learning: Robust Concepts and Random Projection
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
Journal of Computer and System Sciences - Special issu on PODS 2001
Cryptographic hardness for learning intersections of halfspaces
Journal of Computer and System Sciences
Optimal bounds for sign-representing the intersection of two halfspaces by polynomials
Proceedings of the forty-second ACM symposium on Theory of computing
On the hardness of learning intersections of two halfspaces
Journal of Computer and System Sciences
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We give a new algorithm for learning intersections of halfspaces with a margin, i.e. under the assumption that no example lies too close to any separating hyperplane. Our algorithm combines random projection techniques for dimensionality reduction, polynomial threshold function constructions, and kernel methods. The algorithm is fast and simple. It learns a broader class of functions and achieves an exponential runtime improvement compared with previous work on learning intersections of halfspaces with a margin.