Testing (subclasses of) halfspaces

Kevin Matulef*, Ryan O'Donnell, Ronitt Rubinfeld, Rocco Servedio

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


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 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. 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(log n) queries. We complement this lower bound with an upper bound showing that O(√n) queries suffice.

Original languageEnglish
Title of host publicationProperty Testing - Current Research and Surveys
Number of pages7
StatePublished - 2010
Externally publishedYes
EventMini-Workshop on Property Testing - Beijing, China
Duration: 8 Jan 201010 Jan 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6390 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceMini-Workshop on Property Testing


  • halfspaces
  • linear thresholds functions


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