New degree bounds for polynomial threshold functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Learning intersections of halfspaces with a margin
Journal of Computer and System Sciences
Extremal properties of polynomial threshold functions
Journal of Computer and System Sciences
On hardness of learning intersection of two halfspaces
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Polynomials that Sign Represent Parity and Descartes' Rule of Signs
Computational Complexity
A discriminative model for semi-supervised learning
Journal of the ACM (JACM)
Improved lower bounds for learning intersections of halfspaces
COLT'06 Proceedings of the 19th annual conference on Learning Theory
On learning random DNF formulas under the uniform distribution
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
| Hi-index | 0.00 |
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.