TY - JOUR

T1 - Testing that distributions are close

AU - Batu, Tuğkan

AU - Fortnow, Lance

AU - Rubinfeld, Ronitt

AU - Smith, Warren D.

AU - White, Patrick

PY - 2000

Y1 - 2000

N2 - Given two distributions over an n element set, we wish to check whether these distributions are statistically close by only sampling. We give a sublinear algorithm which uses O(n2/3 ε-4 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(ε2/32 qq√n, ε/4√n)) or large (more than ε) in L1-distance. We also give an Ω(n2/3ε-2/3) lower bound. Our algorithm has applications to the problem of checking whether a given Markov process is rapidly mixing. We develop sublinear algorithms for this problem as well).

AB - Given two distributions over an n element set, we wish to check whether these distributions are statistically close by only sampling. We give a sublinear algorithm which uses O(n2/3 ε-4 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(ε2/32 qq√n, ε/4√n)) or large (more than ε) in L1-distance. We also give an Ω(n2/3ε-2/3) lower bound. Our algorithm has applications to the problem of checking whether a given Markov process is rapidly mixing. We develop sublinear algorithms for this problem as well).

UR - http://www.scopus.com/inward/record.url?scp=0034427756&partnerID=8YFLogxK

U2 - 10.1109/SFCS.2000.892113

DO - 10.1109/SFCS.2000.892113

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AN - SCOPUS:0034427756

SP - 259

EP - 269

JO - Annual Symposium on Foundations of Computer Science - Proceedings

JF - Annual Symposium on Foundations of Computer Science - Proceedings

SN - 0272-5428

ER -