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oai:drops-oai.dagstuhl.de:11754 2024-03-06T10:48:37Z ddc:004 open_access

Testing Properties of Multiple Distributions with Few Samples Aliakbarpour, Maryam Silwal, Sandeep Hypothesis Testing Property Testing Distribution Testing Identity Testing Closeness Testing Multiple Sources We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from s distributions, p_1, p_2, …, p_s, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the p_i’s are uniform or ε-far from being uniform in ℓ_1-distance (2) Identity Testing: Testing whether all the p_i’s are equal to an explicitly given distribution q or ε-far from q in ℓ_1-distance, and (3) Closeness Testing: Testing whether all the p_i’s are equal to a distribution q which we have sample access to, or ε-far from q in ℓ_1-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Maryam Aliakbarpour and Sandeep Silwal 2020 Is Part Of LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2020.69 urn:nbn:de:0030-drops-117545 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.69 eng https://creativecommons.org/licenses/by/3.0/legalcode