Testing similar means

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


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.

Original languageEnglish
Title of host publicationAutomata, Languages, and Programming - 39th International Colloquium, ICALP 2012, Proceedings
Number of pages12
EditionPART 1
StatePublished - 2012
Event39th International Colloquium on Automata, Languages, and Programming, ICALP 2012 - Warwick, United Kingdom
Duration: 9 Jul 201213 Jul 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume7391 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference39th International Colloquium on Automata, Languages, and Programming, ICALP 2012
Country/TerritoryUnited Kingdom


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