DROPS

Document

DOI: 10.4230/LIPIcs.ITCS.2025.26

Settling the Complexity of Testing Grainedness of Distributions, and Application to Uniformity Testing in the Huge Object Model

Authors: Clément L. Canonne, Sayantan Sen, and Joy Qiping Yang

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

In this work, we study the problem of testing m-grainedness of probability distributions over an n-element universe 𝒰, or, equivalently, of whether a probability distribution is induced by a multiset S ⊆ 𝒰 of size |S| = m. Recently, Goldreich and Ron (Computational Complexity, 2023) proved that Ω(n^c) samples are necessary for testing this property, for any c < 1 and m = Θ(n). They also conjectured that Ω(m/(log m)) samples are necessary for testing this property when m = Θ(n). In this work, we positively settle this conjecture. Using a known connection to the Distribution over Huge objects (DoHo) model introduced by Goldreich and Ron (TheoretiCS, 2023), we leverage our results to provide improved bounds for uniformity testing in the DoHo model.

Cite as

Clément L. Canonne, Sayantan Sen, and Joy Qiping Yang. Settling the Complexity of Testing Grainedness of Distributions, and Application to Uniformity Testing in the Huge Object Model. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 26:1-26:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{canonne_et_al:LIPIcs.ITCS.2025.26,
  author =	{Canonne, Cl\'{e}ment L. and Sen, Sayantan and Yang, Joy Qiping},
  title =	{{Settling the Complexity of Testing Grainedness of Distributions, and Application to Uniformity Testing in the Huge Object Model}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{26:1--26:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.26},
  URN =		{urn:nbn:de:0030-drops-226543},
  doi =		{10.4230/LIPIcs.ITCS.2025.26},
  annote =	{Keywords: Distribution testing, Uniformity testing, Huge Object Model, Lower bounds}
}

Search Results

Documents authored by Yang, Joy Qiping

Settling the Complexity of Testing Grainedness of Distributions, and Application to Uniformity Testing in the Huge Object Model

Abstract

Cite as

Thanks for your feedback!

Could not send message