Abstract
We initiate the study of differentially private hypothesis testing in the local-model, under both the standard (symmetric) randomized-response mechanism (Warner, 1965; Kasiviswanathan et al., 2008) and the newer (non-symmetric) mechanisms (Bassily & Smith, 2015; Bassily et al., 2017). First, we study the general framework of mapping each user's type into a signal and show that the problem of finding the maximum-likelihood distribution over the signals is feasible. Then we discuss the randomizedresponse mechanism and show that, in essence, it maps the null- and alternative-hypotheses onto new sets, an affine translation of the original sets. We then give sample complexity bounds for identity and independence testing under randomizedresponse. We then move to the newer nonsymmetric mechanisms and show that there too the problem of finding the maximum-likelihood distribution is feasible. Under the mechanism of Bassily et al (2017) we give identity and independence testers with better sample complexity than the testers in the symmetric case, and we also propose a χ2-based identity tester which we investigate empirically.
Original language | English |
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Title of host publication | 35th International Conference on Machine Learning, ICML 2018 |
Editors | Andreas Krause, Jennifer Dy |
Publisher | International Machine Learning Society (IMLS) |
Pages | 7331-7340 |
Number of pages | 10 |
ISBN (Electronic) | 9781510867963 |
State | Published - 2018 |
Externally published | Yes |
Event | 35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden Duration: 10 Jul 2018 → 15 Jul 2018 |
Publication series
Name | 35th International Conference on Machine Learning, ICML 2018 |
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Volume | 10 |
Conference
Conference | 35th International Conference on Machine Learning, ICML 2018 |
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Country/Territory | Sweden |
City | Stockholm |
Period | 10/07/18 → 15/07/18 |
Bibliographical note
Publisher Copyright:© 35th International Conference on Machine Learning, ICML 2018.All Rights Reserved.