Learning intersections and thresholds of halfspaces
Klivans, A.R.
Oapos
Donnell, R.
Dept. of Math., MIT, Cambridge, MA, USA;
This paper appears in: Foundations of Computer Science, 2002. Proceedings. The 43rd Annual IEEE Symposium on
Publication Date: 2002
On page(s): 177- 186
ISSN: 0272-5428
ISBN: 0-7695-1822-2
INSPEC Accession Number: 7567860
Digital Object Identifier: 10.1109/SFCS.2002.1181894
Posted online: 2003-02-28 18:15:24.0
Abstract
We give the first polynomial time algorithm to learn any function of a constant number of halfspaces under the uniform distribution to within any constant error parameter. We also give the first quasipolynomial time algorithm for learning any function of a polylog number of polynomial-weight halfspaces under any distribution. As special cases of these results we obtain algorithms for learning intersections and thresholds of halfspaces. Our uniform distribution learning algorithms involve a novel non-geometric approach to learning halfspaces; we use Fourier techniques together with a careful analysis of the noise sensitivity of functions of halfspaces. Our algorithms for learning under any distribution use techniques from real approximation theory to construct low degree polynomial threshold functions.
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