On the power of conditional samples in distribution testing

Sourav Chakraborty, Eldar Fischer, Yonatan Goldhirsh, Arie Matsliah

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science
Pages561-580
Number of pages20
DOIs
StatePublished - 2013
Event2013 4th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2013 - Berkeley, CA, United States
Duration: 9 Jan 201312 Jan 2013

Publication series

NameITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science

Conference

Conference2013 4th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2013
Country/TerritoryUnited States
CityBerkeley, CA
Period9/01/1312/01/13

Keywords

  • conditional samples
  • distribution testing
  • statistical approximation

All Science Journal Classification (ASJC) codes

  • Management of Technology and Innovation
  • Computer Science (miscellaneous)

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