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41st Annual Symposium on Foundations of Computer Science
Testing that distributions are close
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
T. Batu, L. Fortnow, R. Rubinfeld, W.D. Smith, P. White, "Testing that distributions are close," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 259, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892113, author = {T. Batu and L. Fortnow and R. Rubinfeld and W.D. Smith and P. White}, title = {Testing that distributions are close}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {259}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892113}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Testing that distributions are close SN  02725428 SP EP A1  T. Batu, A1  L. Fortnow, A1  R. Rubinfeld, A1  W.D. Smith, A1  P. White, PY  2000 KW  sampling methods; Markov processes; probability; computational complexity; distribution closeness testing; sampling; sublinear algorithm; lower bound; Markov process; rapidly mixing process; sublinear algorithms; probability VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
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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