Learning symmetric k-juntas in time n^o(k)
Combinatorics
2007-05-23 v1
Abstract
We give an algorithm for learning symmetric k-juntas (boolean functions of boolean variables which depend only on an unknown set of of these variables) in the PAC model under the uniform distribution, which runs in time n^{O(k/\log k)}. Our bound is obtained by proving the following result: Every symmetric boolean function on k variables, except for the parity and the constant functions, has a non-zero Fourier coefficient of order at least 1 and at most O(k/\log k). This improves the previously best known bound of (3/31)k, and provides the first n^{o(k)} time algorithm for learning symmetric juntas.
Cite
@article{arxiv.math/0504246,
title = {Learning symmetric k-juntas in time n^o(k)},
author = {Mihail N. Kolountzakis and Evangelos Markakis and Aranyak Mehta},
journal= {arXiv preprint arXiv:math/0504246},
year = {2007}
}