On learning a union of half spaces
Journal of Complexity
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COLT '90 Proceedings of the third annual workshop on Computational learning theory
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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
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Learning an intersection of k halfspaces over a uniform distribution
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
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FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Baum's Algorithm Learns Intersections of Halfspaces with Respect to Log-Concave Distributions
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
The Intersection of Two Halfspaces Has High Threshold Degree
FOCS '09 Proceedings of the 2009 50th 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
Random direction divisive clustering
Pattern Recognition Letters
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We give an algorithm to learn an intersection of k halfspaces in Rn whose normals span an l-dimensional subspace. For any input distribution with a logconcave density such that the bounding hyperplanes of the k halfspaces pass through its mean, the algorithm (&epsis;,δ)-learns with time and sample complexity bounded by (nkl/&epsis;)O(l) log 1/&epsis; δ. The hypothesis found is an intersection of O(k log (1/&epsis;)) halfspaces. This improves on Blum and Kannan's algorithm for the uniform distribution over a ball, in the time and sample complexity (previously doubly exponential) and in the generality of the input distribution.