Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
The Strength of Weak Learnability
Machine Learning
Computing nearest neighbor pattern classification perceptrons
Information Sciences—Intelligent Systems: An International Journal
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
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Principal Component Analysis over Continuous Subspaces and Intersection of Half-Spaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Hardness Results for Coloring 3 -Colorable 3 -Uniform Hypergraphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Learning Intersections and Thresholds of Halfspaces
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Training a 3-Node Neural Network is NP-Complete
Machine Learning: From Theory to Applications - Cooperative Research at Siemens and MIT
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
An Algorithmic Theory of Learning: Robust Concepts and Random Projection
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A polynomial-time algorithm for learning noisy linear threshold functions
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A new PCP outer verifier with applications to homogeneous linear equations and max-bisection
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Learnability and Automatizability
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantitative Association Rules Based on Half-Spaces: An Optimization Approach
ICDM '04 Proceedings of the Fourth IEEE International Conference on Data Mining
Agnostically Learning Halfspaces
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A 3-Query Non-Adaptive PCP with Perfect Completeness
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Hardness of Learning Halfspaces with Noise
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Cryptographic Hardness for Learning Intersections of Halfspaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
New Results for Learning Noisy Parities and Halfspaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Hardness of Reconstructing Multivariate Polynomials over Finite Fields
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Optimal bounds for sign-representing the intersection of two halfspaces by polynomials
Proceedings of the forty-second ACM symposium on Theory of computing
Hardness of Reconstructing Multivariate Polynomials over Finite Fields
SIAM Journal on Computing
On unique games with negativeweights
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Bypassing UGC from some optimal geometric inapproximability results
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Hardness results for agnostically learning low-degree polynomial threshold functions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We show that unless NP = RP, it is hard to (even) weakly PAC-learn intersection of two halfspaces in Rn using a hypothesis which is a function of up to l linear threshold functions for any integer l. Specifically, we show that for every integer l and an arbitrarily small constant ε 0, unless NP = RP, no polynomial time algorithm can distinguish whether there is an intersection of two halfspaces that correctly classifies a given set of labeled points in Rn, or whether any function of l linear threshold functions can correctly classify at most 1/2+ε fraction of the points.