Title
Date of Original Version
7-2009
Type
Article
Published In
SIAM J. Comput. Volume 39, Issue 5, pp. 2004-2047 (2010)
Abstract or Table of Contents
This paper addresses the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x) = sgn(w∙x−Θ):We consider halfspaces over the continuous domain Rn (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean cube {-1; 1}n (endowed with the uniform distribution). In both cases we give an algorithm that distinguishes halfspaces from functions that are ε-far from any halfspace using only poly( 1/ε) queries, independent of the dimension n.