文章基本信息

标题：Testing Shape Restrictions of Discrete Distributions
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作者：Cl{\'e}ment L. Canonne ; Ilias Diakonikolas ; Themis Gouleakis 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：47
页码：25:1-25:14
DOI：10.4230/LIPIcs.STACS.2016.25
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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 in P and l_{1}(D,P)>epsilon. 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.
关键词：property testing; probability distributions; statistics; lower bounds