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41st Annual Symposium on Foundations of Computer Science
Testing that distributions are close
Redondo Beach, California
November 12-November 14
ISBN: 0-7695-0850-2
T. Batu, Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA
L. Fortnow, Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA
R. Rubinfeld, Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA
W.D. Smith, Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA
P. White, Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA
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(n/sup 2/3//spl epsiv//sup -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(/spl epsiv//sup 2//32/sup 3//spl radic/n,/spl epsiv//4/spl radic/n=)) or large (more than /spl epsiv/) in L/sub 1/-distance. We also give an /spl Omega/(n/sup 2/3//spl epsiv//sup -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.
Index Terms:
sampling methods; Markov processes; probability; computational complexity; distribution closeness testing; sampling; sublinear algorithm; lower bound; Markov process; rapidly mixing process; sublinear algorithms; probability
Citation:
T. Batu, L. Fortnow, R. Rubinfeld, W.D. Smith, P. White, "Testing that distributions are close," focs, pp.259, 41st Annual Symposium on Foundations of Computer Science, 2000
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