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dc.contributor.authorBun, Marken_US
dc.contributor.authorKamath, Gautamen_US
dc.contributor.authorSteinke, Thomasen_US
dc.contributor.authorWu, Zhiwei Stevenen_US
dc.date.accessioned2021-11-03T13:28:07Z
dc.date.available2021-11-03T13:28:07Z
dc.date.issued2021-03
dc.identifier.citationM. Bun, G. Kamath, T. Steinke, Z.S. Wu. 2021. "Private Hypothesis Selection." IEEE Transactions on Information Theory, Volume 67, Issue 3, pp. 1981 - 2000. https://doi.org/10.1109/tit.2021.3049802
dc.identifier.issn0018-9448
dc.identifier.issn1557-9654
dc.identifier.urihttps://hdl.handle.net/2144/43258
dc.description.abstractWe provide a differentially private algorithm for hypothesis selection. Given samples from an unknown probability distribution P and a set of m probability distributions H, the goal is to output, in a ε-differentially private manner, a distribution from H whose total variation distance to P is comparable to that of the best such distribution (which we denote by α). The sample complexity of our basic algorithm is O(log m/α^2 + log m/αε), representing a minimal cost for privacy when compared to the non-private algorithm. We also can handle infinite hypothesis classes H by relaxing to (ε, δ)-differential privacy. We apply our hypothesis selection algorithm to give learning algorithms for a number of natural distribution classes, including Gaussians, product distributions, sums of independent random variables, piecewise polynomials, and mixture classes. Our hypothesis selection procedure allows us to generically convert a cover for a class to a learning algorithm, complementing known learning lower bounds which are in terms of the size of the packing number of the class. As the covering and packing numbers are often closely related, for constant α, our algorithms achieve the optimal sample complexity for many classes of interest. Finally, we describe an application to private distribution-free PAC learning.en_US
dc.description.urihttps://arxiv.org/abs/1905.13229
dc.format.extentp. 1981 - 2000en_US
dc.language.isoen_US
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en_US
dc.relation.ispartofIEEE Transactions on Information Theory
dc.subjectComplexity theoryen_US
dc.subjectPrivacyen_US
dc.subjectDifferential privacyen_US
dc.subjectApproximation algorithmsen_US
dc.subjectTVen_US
dc.subjectPicture archiving and communication systemsen_US
dc.subjectInterneten_US
dc.titlePrivate hypothesis selectionen_US
dc.typeArticleen_US
dc.identifier.doi10.1109/tit.2021.3049802
pubs.elements-sourcecrossrefen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Computer Scienceen_US
pubs.publication-statusPublisheden_US
dc.identifier.mycv617034


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