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 -