TY - GEN

T1 - Testing similar means

AU - Levi, Reut

AU - Ron, Dana

AU - Rubinfeld, Ronitt

PY - 2012

Y1 - 2012

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 (measured according to the ℓ1 distance averaged over the distributions) 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 m 1-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 (measured according to the ℓ1 distance averaged over the distributions) 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 m 1-poly(ε), where m is the number of distributions.

UR - http://www.scopus.com/inward/record.url?scp=84883789634&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-31594-7_53

DO - 10.1007/978-3-642-31594-7_53

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AN - SCOPUS:84883789634

SN - 9783642315930

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 629

EP - 640

BT - Automata, Languages, and Programming - 39th International Colloquium, ICALP 2012, Proceedings

T2 - 39th International Colloquium on Automata, Languages, and Programming, ICALP 2012

Y2 - 9 July 2012 through 13 July 2012

ER -