Testing Shape Restrictions of Discrete Distributions
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Testing shape.pdf
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Author(s)
Canonne, Clément L.
Diakonikolas, Ilias
Gouleakis, Themistoklis
Rubinfeld, Ronitt
Date Issued
February 2016
Journal
33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Publisher
Dagstuhl Publishing
Citation
Canonne, Clément L. et al. "Testing Shape Restrictions of Discrete Distributions." 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016), February 17-20, 2016, Orléans, France, Dagstuhl Publishing, February 2016 © Clément L. Canonne, Ilias Diakonikolas, Themis Gouleakis,
and Ronitt Rubinfeld
Version
Final published version
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 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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution 4.0 International License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.STACS.2016.25
