research-article

On the power of conditional samples in distribution testing

Authors:

Sourav Chakraborty,

Eldar Fischer,

Yonatan Goldhirsh,

Arie MatsliahAuthors Info & Claims

ITCS '13: Proceedings of the 4th conference on Innovations in Theoretical Computer Science

Pages 561 - 580

https://doi.org/10.1145/2422436.2422497

Published: 09 January 2013 Publication History

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Abstract

In this paper we define and examine the power of the conditional sampling oracle in the context of distribution-property testing. The conditional sampling oracle for a discrete distribution μ takes as input a subset S ⊂ [n] of the domain, and outputs a random sample i ∈ S drawn according to μ, conditioned on S (and independently of all prior samples). The conditional-sampling oracle is a natural generalization of the ordinary sampling oracle in which S always equals [n]. We show that with the conditional-sampling oracle, testing uniformity, testing identity to a known distribution, and testing any label-invariant property of distributions is easier than with the ordinary sampling oracle. On the other hand, we also show that for some distribution properties the sample complexity remains near-maximal even with conditional sampling.

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Cited By

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Berg TOrdentlich OShayevitz O(2024)Statistical Inference With Limited Memory: A SurveyIEEE Journal on Selected Areas in Information Theory10.1109/JSAIT.2024.34812965(623-644)Online publication date: 2024
https://doi.org/10.1109/JSAIT.2024.3481296
Havlicek V(2023)Amplitude Ratios and Neural Network Quantum StatesQuantum10.22331/q-2023-03-02-9387(938)Online publication date: 2-Mar-2023
https://doi.org/10.22331/q-2023-03-02-938
Fotakis DKalavasis ATzamos C(2022)Efficient Parameter Estimation of Truncated Boolean Product DistributionsAlgorithmica10.1007/s00453-022-00961-984:8(2186-2221)Online publication date: 22-Apr-2022
https://doi.org/10.1007/s00453-022-00961-9
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Index Terms

On the power of conditional samples in distribution testing
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic algorithms
    2. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods
      2. Sequential Monte Carlo methods
2. Theory of computation
  1. Models of computation
    1. Probabilistic computation
  2. Randomness, geometry and discrete structures

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Published In

ITCS '13: Proceedings of the 4th conference on Innovations in Theoretical Computer Science

January 2013

594 pages

ISBN:9781450318594

DOI:10.1145/2422436

Program Chair:
Robert Kleinberg
Cornell University

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

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Published: 09 January 2013

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ITCS '13

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SIGACT

ITCS '13: Innovations in Theoretical Computer Science

January 9 - 12, 2013

California, Berkeley, USA

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Overall Acceptance Rate 172 of 513 submissions, 34%

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Cited By

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Berg TOrdentlich OShayevitz O(2024)Statistical Inference With Limited Memory: A SurveyIEEE Journal on Selected Areas in Information Theory10.1109/JSAIT.2024.34812965(623-644)Online publication date: 2024
https://doi.org/10.1109/JSAIT.2024.3481296
Havlicek V(2023)Amplitude Ratios and Neural Network Quantum StatesQuantum10.22331/q-2023-03-02-9387(938)Online publication date: 2-Mar-2023
https://doi.org/10.22331/q-2023-03-02-938
Fotakis DKalavasis ATzamos C(2022)Efficient Parameter Estimation of Truncated Boolean Product DistributionsAlgorithmica10.1007/s00453-022-00961-984:8(2186-2221)Online publication date: 22-Apr-2022
https://doi.org/10.1007/s00453-022-00961-9
Canonne CChen XKamath GLevi AWaingarten EMarx D(2021)Random restrictions of high dimensional distributions and uniformity testing with subcube conditioningProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458085(321-336)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458085
Kamath GTzamos CChan T(2019)AnacondaProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310478(679-693)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310478
Blais ECanonne CGur T(2019)Distribution Testing Lower Bounds via Reductions from Communication ComplexityACM Transactions on Computation Theory10.1145/330527011:2(1-37)Online publication date: 11-Feb-2019
https://dl.acm.org/doi/10.1145/3305270
Canonne CDiakonikolas IGouleakis TRubinfeld R(2018)Testing Shape Restrictions of Discrete DistributionsTheory of Computing Systems10.1007/s00224-017-9785-662:1(4-62)Online publication date: 1-Jan-2018
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Blais ECanonne CGur T(2017)Distribution testing lower bounds via reductions from communication complexityProceedings of the 32nd Computational Complexity Conference10.5555/3135595.3135623(1-40)Online publication date: 9-Jul-2017
https://dl.acm.org/doi/10.5555/3135595.3135623
Gouleakis TTzamos CZampetakis MKlein P(2017)Faster sublinear algorithms using conditional samplingProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039800(1743-1757)Online publication date: 16-Jan-2017
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Ron DTsur G(2016)The Power of an ExampleACM Transactions on Computation Theory10.1145/29306578:4(1-19)Online publication date: 14-Jun-2016
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