Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



TR12-055 | 4th May 2012 23:10

Testing Similar Means


Authors: Reut Levi, Dana Ron, Ronitt Rubinfeld
Publication: 5th May 2012 00:01
Downloads: 3812


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 $\ell_1$ 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 $1/\epsilon$ (where $\epsilon$ is the given distance parameter). While in the sampling model, the complexity grows roughly as $m^{1-{\rm poly}(\epsilon)}$, where $m$ is the number of distributions.

ISSN 1433-8092 | Imprint