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Testing closeness of discrete distributions

Batu, Tugkan and Fortnow, Lance and Rubinfeld, Ronitt and Smith, Warren D. and White, Patrick (2010) Testing closeness of discrete distributions. arXiv.org.

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Abstract

Given samples from two distributions over an $n$-element set, we wish to test whether these distributions are statistically close. We present an algorithm which uses sublinear in $n$, specifically, $O(n^{2/3}\epsilon^{-8/3}\log n)$, independent samples from each distribution, runs in time linear in the sample size, makes no assumptions about the structure of the distributions, and distinguishes the cases when the distance between the distributions is small (less than $\max\{\epsilon^{4/3}n^{-1/3}/32, \epsilon n^{-1/2}/4\}$) or large (more than $\epsilon$) in $\ell_1$ distance. This result can be compared to the lower bound of $\Omega(n^{2/3}\epsilon^{-2/3})$ for this problem given by Valiant. Our algorithm has applications to the problem of testing whether a given Markov process is rapidly mixing. We present sublinear for several variants of this problem as well. A preliminary version of this paper appeared in the 41st Symposium on Foundations of Computer Science, 2000, Redondo Beach, CA

Item Type: Monograph (Report)
Official URL: http://arxiv.org/abs/1009.5397v1
Additional Information: © 2010 The authors
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 10 Jan 2011 10:10
Last Modified: 10 Jan 2011 10:11
URI: http://eprints.lse.ac.uk/id/eprint/31299

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