Affiliation:
1. London School of Economics and Political Science
2. Northwestern University
3. Massachusetts Institute of Technology and Tel Aviv University
4. Center for Range Voting
Abstract
Given samples from two distributions over an
n
-element set, we wish to test whether these distributions are statistically close. We present an algorithm which uses sublinear in
n
, specifically,
O
(
n
2/3
ε
−8/3
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 {
ε
4/3
n
−1/3
/32,
εn
−1/2
/4}) or large (more than
ε
) in ℓ
1
distance. This result can be compared to the lower bound of
Ω
(
n
2/3
ε
−2/3
) for this problem given by Valiant [2008].
Our algorithm has applications to the problem of testing whether a given Markov process is rapidly mixing. We present sublinear algorithms for several variants of this problem as well.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference57 articles.
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