Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning

Clément L. Canonne; Xi Chen; Gautam Kamath; Amit Levi; Erik Waingarten

Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning

Clément L. Canonne
, Xi Chen
, Gautam Kamath
, Amit Levi
, Erik Waingarten

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We give a nearly-optimal algorithm for testing uniformity of distributions supported on {−1,1}ⁿ, which makes O^e(√n/ε²) many queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)). The key technical component is a natural notion of random restrictions for distributions on {−1,1}ⁿ, and a quantitative analysis of how such a restriction affects the mean vector of the distribution. Along the way, we consider the problem of mean testing with independent samples and provide a nearly-optimal algorithm.

Original language	English
Title of host publication	ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Editors	Daniel Marx
Publisher	Association for Computing Machinery
Pages	321-336
Number of pages	16
ISBN (Electronic)	9781611976465
State	Published - 2021
Externally published	Yes
Event	32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States Duration: 10 Jan 2021 → 13 Jan 2021

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference	32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Country/Territory	United States
City	Alexandria, Virtual
Period	10/01/21 → 13/01/21

Bibliographical note

Publisher Copyright:
Copyright © 2021 by SIAM

ASJC Scopus subject areas

Software
General Mathematics

Cite this

Canonne, C. L., Chen, X., Kamath, G., Levi, A., & Waingarten, E. (2021). Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning. In D. Marx (Ed.), ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 (pp. 321-336). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery.

@inproceedings{67ba6415349b469ea3b363b351db3e04,

title = "Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning",

abstract = "We give a nearly-optimal algorithm for testing uniformity of distributions supported on \{−1,1\}n, which makes Oe(√n/ε2) many queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)). The key technical component is a natural notion of random restrictions for distributions on \{−1,1\}n, and a quantitative analysis of how such a restriction affects the mean vector of the distribution. Along the way, we consider the problem of mean testing with independent samples and provide a nearly-optimal algorithm.",

author = "Canonne, \{Cl{\'e}ment L.\} and Xi Chen and Gautam Kamath and Amit Levi and Erik Waingarten",

note = "Publisher Copyright: Copyright {\textcopyright} 2021 by SIAM; 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 ; Conference date: 10-01-2021 Through 13-01-2021",

year = "2021",

language = "English",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery",

pages = "321--336",

editor = "Daniel Marx",

booktitle = "ACM-SIAM Symposium on Discrete Algorithms, SODA 2021",

address = "United States",

}

Canonne, CL, Chen, X, Kamath, G, Levi, A & Waingarten, E 2021, Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning. in D Marx (ed.), ACM-SIAM Symposium on Discrete Algorithms, SODA 2021. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, pp. 321-336, 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, Alexandria, Virtual, United States, 10/01/21.

Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning. / Canonne, Clément L.; Chen, Xi; Kamath, Gautam et al.
ACM-SIAM Symposium on Discrete Algorithms, SODA 2021. ed. / Daniel Marx. Association for Computing Machinery, 2021. p. 321-336 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Chen, Xi

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AU - Levi, Amit

AU - Waingarten, Erik

PY - 2021

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AB - We give a nearly-optimal algorithm for testing uniformity of distributions supported on {−1,1}n, which makes Oe(√n/ε2) many queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)). The key technical component is a natural notion of random restrictions for distributions on {−1,1}n, and a quantitative analysis of how such a restriction affects the mean vector of the distribution. Along the way, we consider the problem of mean testing with independent samples and provide a nearly-optimal algorithm.

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M3 - Conference contribution

AN - SCOPUS:85105332536

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

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BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2021

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ER -

Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

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Cite this