Lp-testing

Piotr Berman, Sofya Raskhodnikova, Grigory Yaroslavtsev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

34 Scopus citations

Abstract

We initiate a systematic study of sublinear algorithms for approximately testing properties of real-valued data with respect to Lp distances. Such algorithms distinguish datasets which either have (or are close to having) a certain property from datasets which are far from having it with respect to Lp distance. For applications involving noisy realvalued data, using Lp distances allows algorithms to withstand noise of bounded L p norm. While the classical property testing framework developed with respect to Hamming distance has been studied extensively, testing with respect to Lp distances has received little attention. We use our framework to design simple and fast algorithms for classic problems, such as testing monotonicity, convexity and the Lipschitz property, and also distance approximation to monotonicity. In particular, for functions over the hypergrid domains [n]d, the complexity of our algorithms for all these properties does not depend on the linear dimension n. This is impossible in the standard model. Most of our algorithms require minimal assumptions on the choice of sampled data: either uniform or easily samplable random queries suffice. We also show connections between the Lp-testing model and the standard framework of property testing with respect to Hamming distance. Some of our results improve existing bounds for Hamming distance.

Original languageEnglish (US)
Title of host publicationSTOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Pages164-173
Number of pages10
ISBN (Print)9781450327107
DOIs
StatePublished - Jan 1 2014
Event4th Annual ACM Symposium on Theory of Computing, STOC 2014 - New York, NY, United States
Duration: May 31 2014Jun 3 2014

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Other

Other4th Annual ACM Symposium on Theory of Computing, STOC 2014
CountryUnited States
CityNew York, NY
Period5/31/146/3/14

All Science Journal Classification (ASJC) codes

  • Software

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