Batu, Tugkan, Fortnow, L., Rubinfeld, R., Smith, W. D. and White, P.
(2000)
*Testing that distributions are close.*
In:
Proceedings 41st Annual Symposium on Foundations of Computer Science.
IEEE, New York, USA, pp. 259-269.

## 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(n2/3ε-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(ε2/323 √n,ε/4√n=)) or large (more than ε) in L 1-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.

Item Type: | Book Section |
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Official URL: | http://www.computer.org/portal/web/csdl/abs/procee... |

Additional Information: | © 2000 IEEE |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science |

Sets: | Departments > Mathematics |

Date Deposited: | 04 Jan 2011 13:46 |

Last Modified: | 20 Feb 2019 04:35 |

URI: | http://eprints.lse.ac.uk/id/eprint/31082 |

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