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Testing closeness of discrete distributions

Batu, Tugkan ORCID: 0000-0003-3914-4645, Fortnow, Lance, Rubinfeld, Ronitt, Smith, Warren D. and White, Patrick (2013) Testing closeness of discrete distributions. Journal of the ACM, 60 (1). ISSN 0004-5411

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Identification Number: 10.1145/2432622.2432626


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 ( n2/3ε -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 { ε4/3n-1/3/32, εn-1/2/4 }) or large (more than ε) in ℓ1 distance. This result can be compared to the lower bound of Ω ( n 2/3ε -2/3 ) for this problem given by Valiant [2008]. Our algorithm has applications to the problem of testing whether a given Markov process is rapidly mixing. We present sublinear algorithms for several variants of this problem as well.

Item Type: Article
Official URL:
Additional Information: © 2013 Association of Computing Machinery
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 27 Mar 2013 16:58
Last Modified: 09 Jul 2024 07:36

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