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Testing Data Binnings

Authors Clément L. Canonne , Karl Wimmer

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  • Theory of computation → Machine learning theory
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • property testing
  • distribution testing
  • identity testing
  • hypothesis testing

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Abstract

Motivated by the question of data quantization and "binning," we revisit the problem of identity testing of discrete probability distributions. Identity testing (a.k.a. one-sample testing), a fundamental and by now well-understood problem in distribution testing, asks, given a reference distribution (model) 𝐪 and samples from an unknown distribution 𝐩, both over [n] = {1,2,… ,n}, whether 𝐩 equals 𝐪, or is significantly different from it.
In this paper, we introduce the related question of identity up to binning, where the reference distribution 𝐪 is over k ≪ n elements: the question is then whether there exists a suitable binning of the domain [n] into k intervals such that, once "binned," 𝐩 is equal to 𝐪. We provide nearly tight upper and lower bounds on the sample complexity of this new question, showing both a quantitative and qualitative difference with the vanilla identity testing one, and answering an open question of Canonne [Clément L. Canonne, 2019]. Finally, we discuss several extensions and related research directions.

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Clément L. Canonne and Karl Wimmer. Testing Data Binnings. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2020.24

Author Details

Clément L. Canonne
  • IBM Research, Almaden, CA, USA
Karl Wimmer
  • Duquesne University, Pittsburgh, PA, USA

References

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