Testing shape restrictions of discrete distributions

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations

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 ℓ1(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 publication33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016
EditorsHeribert Vollmer, Nicolas Ollinger
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770019
DOIs
StatePublished - 1 Feb 2016
Event33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016 - Orleans, France
Duration: 17 Feb 201620 Feb 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume47
ISSN (Print)1868-8969

Conference

Conference33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016
Country/TerritoryFrance
CityOrleans
Period17/02/1620/02/16

Funding

FundersFunder number
National Science Foundation
Directorate for Computer and Information Science and Engineering1319788, 1115703

    Keywords

    • Lower bounds
    • Probability distributions
    • Property testing
    • Statistics

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