2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2002)
Vancouver, BC, Canada
Nov. 16, 2002 to Nov. 19, 2002
Rocco A. Servedio , Harvard University
Adam R. Klivans , Massachusetts Institute of Technology
Ryan O?Donnell , Massachusetts Institute of Technology
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.
Rocco A. Servedio, Adam R. Klivans, Ryan O?Donnell, "Learning Intersections and Thresholds of Halfspaces", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 177, 2002, doi:10.1109/SFCS.2002.1181894