A Random Sampling based Algorithm for Learning the Intersection of Half-spaces

Authors:
Santosh Vempala
Affiliations:
-
Venue:
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Year:
1997

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Abstract

We present an algorithm for learning the intersection of half-spaces in n dimensions. Over nearly-uniform distributions, it runs in polynomial time for up to O(log n /log log n) half-spaces or, more generally, for any number of half-spaces whose normal vectors lie in an O(log n / log log n) dimensional subspace. Over less restricted ``non-concentrated'' distributions it runs in polynomial time for a constant number of half-spaces. This generalizes an earlier result of Blum and Kannan. The algorithm is simple and is based on random sampling.