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Testing random variables for independence and identity

Batu, Tugkan and Fischer, E. and Fortnow, L. and Kumar, R. and Rubinfeld, R. and White, P. (2001) Testing random variables for independence and identity. In: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (Focs). Foundations of Computer Science. IEEE, New York, USA, pp. 442-451.

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Identification Number: 10.1109/SFCS.2001.959920

Abstract

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 L1 norm to the product distribution A1 × A2 for some distributions A1 over [n] and A2 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. Furthermore, given access to samples of a distribution X over [n], we show how to test if X is \varepsilon-close in L1 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.

Item Type: Book Section
Official URL: http://www.computer.org/portal/web/csdl/abs/procee...
Additional Information: © 2002 IEEE
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Sets: Departments > Mathematics
Date Deposited: 05 Jan 2011 12:42
Last Modified: 10 Jan 2011 09:36
URI: http://eprints.lse.ac.uk/id/eprint/31083

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