Testing (subclasses of) halfspaces
Author(s)
Matulef, Kevin M.
O'Donnell, Ryan
Rubinfeld, Ronitt
Servedio, Rocco
Date Issued
January 2010
Journal
Proceedings of the ITCS Mini-workshop on Property Testing (2010 : Beijing, China)
Publisher
Springer-Verlag
Citation
Matulef, Kevin et al. “Testing (Subclasses of) Halfspaces.” Property Testing. Ed. Oded Goldreich. (Lecture Notes in Computer Science : Vol. 6390). Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. 334–340.
Version
Author's final manuscript
Abstract
We address 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 R n (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) queries, independent of the dimension n.
In contrast to the case of general halfspaces, we show that testing natural subclasses of halfspaces can be markedly harder; for the class of { − 1,1}-weight halfspaces, we show that a tester must make at least Ω(logn) queries. We complement this lower bound with an upper bound showing that O(√n) queries suffice.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/978-3-642-16367-8_27
