Testing Shape Restrictions of Discrete Distributions

Clément L. Canonne, Ilias Diakonikolas, Themis Gouleakis, Ronitt Rubinfeld

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

Abstract

We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution D over [n] and a property P, the goal is to distinguish between D ∈ P and `1(D,P) > ε. We develop a general algorithm for this question, which applies to a large range of “shape-constrained” properties, including monotone,log-concave, t-modal, piecewise-polynomial, and Poisson Binomial distributions. Moreover, for all cases considered, our algorithm has near-optimal sample complexity with regard to the domain size and is computationally efficient. For most of these classes, we provide the first non-trivial tester in the literature. In addition, we also describe a generic method to prove lower bounds for this problem, and use it to show our upper bounds are nearly tight. Finally, we extend some of our techniques to tolerant testing, deriving nearly–tight upper and lower bounds for the corresponding questions.
Original languageEnglish
Title of host publicationProceedings of the 33rd International Symposium on Theoretical Aspects of Computer Science (STACS 2016)
PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany
Pages1-14
Number of pages14
ISBN (Print)978-3-95977-001-9
DOIs
Publication statusPublished - 2016
Event33rd International Symposium on Theoretical Aspects of Computer Science - Orléans, France
Duration: 17 Feb 201620 Feb 2016
http://www.univ-orleans.fr/lifo/events/STACS2016/

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Volume47
ISSN (Print)1868-8969

Conference

Conference33rd International Symposium on Theoretical Aspects of Computer Science
Abbreviated titleSTACS 2016
Country/TerritoryFrance
CityOrléans
Period17/02/1620/02/16
Internet address

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