TY - JOUR

T1 - Testing similar means

AU - Levi, Reut

AU - Ron, Dana

AU - Rubinfeld, Ronitt

N1 - Publisher Copyright:
© 2014 Society for Industrial and Applied Mathematics.

PY - 2014

Y1 - 2014

N2 - We consider the problem of testing a basic property of collections of distributions: having similar means. Namely, the algorithm should accept collections of distributions in which all distributions have means that do not differ by more than some given parameter and should reject collections that are relatively far from having this property. By "far" we mean that it is necessary to modify the distributions in a relatively significant manner (according to some predetermined distance measure) so as to obtain the property. We study this problem in two models. In the first model (the query model) the algorithm may ask for samples from any distribution of its choice, and in the second model (the sampling model) the distributions from which it gets samples are selected randomly. We provide upper and lower bounds in both models. In particular, in the query model, the complexity of the problem is polynomial in 1/ε (where ε is the given distance parameter), while in the sampling model, the complexity grows roughly as m1-poly(ε), where m is the number of distributions.

AB - We consider the problem of testing a basic property of collections of distributions: having similar means. Namely, the algorithm should accept collections of distributions in which all distributions have means that do not differ by more than some given parameter and should reject collections that are relatively far from having this property. By "far" we mean that it is necessary to modify the distributions in a relatively significant manner (according to some predetermined distance measure) so as to obtain the property. We study this problem in two models. In the first model (the query model) the algorithm may ask for samples from any distribution of its choice, and in the second model (the sampling model) the distributions from which it gets samples are selected randomly. We provide upper and lower bounds in both models. In particular, in the query model, the complexity of the problem is polynomial in 1/ε (where ε is the given distance parameter), while in the sampling model, the complexity grows roughly as m1-poly(ε), where m is the number of distributions.

KW - Property testing of distributions

KW - Sublinear-time algorithms

UR - http://www.scopus.com/inward/record.url?scp=84919880059&partnerID=8YFLogxK

U2 - 10.1137/120903737

DO - 10.1137/120903737

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AN - SCOPUS:84919880059

SN - 0895-4801

VL - 28

SP - 1699

EP - 1724

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 4

ER -