2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2000)

Redondo Beach, California

Nov. 12, 2000 to Nov. 14, 2000

ISSN: 0272-5428

ISBN: 0-7695-0850-2

pp: 259

T. Batu , Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA

W.D. Smith , 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

P. White , Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA

ABSTRACT

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,
W.D. Smith,
L. Fortnow,
R. Rubinfeld,
P. White,
"Testing that distributions are close",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 259, 2000, doi:10.1109/SFCS.2000.892113SEARCH