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Generalized uniformity testing

Batu, Tugkan and Canonne, Clément L. (2017) Generalized uniformity testing. In: Proceedings of the Annual Symposium on Foundations of Computer Science. IEEE Computer Society, Washington, USA. (In Press)

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Abstract

In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and is by now fully understood. The complexity of deciding whether an unknown distribution is uniform over its unknown (and arbitrary) support, however, is much less clear. Yet, this task arises as soon as no prior knowledge on the domain is available, or whenever the samples originate from an unknown and unstructured universe. In this work, we introduce and study this generalized uniformity testing question, and establish nearly tight upper and lower bound showing that – quite surprisingly – its sample complexity significantly differs from the known-domain case. Moreover, our algorithm is intrinsically adaptive, in contrast to the overwhelming majority of known distribution testing algorithms.

Item Type: Book Section
Official URL: http://ieee-focs.org/
Additional Information: © 2017 IEEE
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Sets: Departments > Mathematics
Date Deposited: 22 Aug 2017 11:07
Last Modified: 22 Aug 2017 13:31
URI: http://eprints.lse.ac.uk/id/eprint/84067

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