Learning Intersections and Thresholds of Halfspaces
| Citations: | 51 - 17 self |
BibTeX
@MISC{Klivans_learningintersections,
author = {Adam R. Klivans and Ryan O'Donnell and Rocco A. Servedio},
title = {Learning Intersections and Thresholds of Halfspaces},
year = {}
}
Years of Citing Articles
OpenURL
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.







