Proceedings 2001 IEEE International Conference on Cluster Computing (2001)
Oct. 14, 2001 to Oct. 17, 2001
ISBN: 0-7695-1390-5
pp: 442
ABSTRACT
<p>Given access to independent samples of a distribution A over [n] × [m], we show how to test whether the distributions formed by projecting A to each coordinate are independent, i.e., whether A is \varepsilon-close in the L<sub>1</sub> norm to the product distribution A<sub>1</sub> × A<sub>2</sub> for some distributions A<sub>1</sub> over [n] and A<sub>2</sub> over [m]. The sample complexity of our test is \widetilde0(n^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} m^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} poly(\varepsilon ^{ - 1} )), assuming without loss of generality that m \leqslant n. We also give a matching lower bound, up to poly(\log n,\varepsilon ^{ - 1} ) factors.</p> <p>Furthermore, given access to samples of a distribution X over [n], we show how to test if X is \varepsilon-close in L<sub>1</sub> norm to an explicitly specified distribution Y . Our test uses \widetilde0(n^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} poly(\varepsilon ^{ - 1} )) samples, which nearly matches the known tight bounds for the case when Y is uniform.</p>
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CITATION

E. Fischer, T. Batu, R. Kumar, R. Rubinfeld, P. White and L. Fortnow, "Testing Random Variables for Independence and Identity," Proceedings 2001 IEEE International Conference on Cluster Computing(FOCS), Las Vegas, Nevada, 2001, pp. 442.
doi:10.1109/SFCS.2001.959920