TY - GEN
T1 - Testing (subclasses of) halfspaces
AU - Matulef, Kevin
AU - O'Donnell, Ryan
AU - Rubinfeld, Ronitt
AU - Servedio, Rocco
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
KW - halfspaces
KW - linear thresholds functions
UR - http://www.scopus.com/inward/record.url?scp=78449296576&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-16367-8_27
DO - 10.1007/978-3-642-16367-8_27
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:78449296576
SN - 3642163661
SN - 9783642163661
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 334
EP - 340
BT - Property Testing - Current Research and Surveys
T2 - Mini-Workshop on Property Testing
Y2 - 8 January 2010 through 10 January 2010
ER -