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Testing Similar Means

  • Reut Levi
  • Dana Ron
  • Ronitt Rubinfeld
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)

Abstract

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.

Keywords

Success Probability Sample Complexity Basic Algorithm Chebyshev Polynomial Sampling Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Reut Levi
    • 1
  • Dana Ron
    • 1
  • Ronitt Rubinfeld
    • 1
    • 2
  1. 1.Tel Aviv UniversityIsrael
  2. 2.MITUSA

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