Differentially Private Algorithms for Learning Mixtures of Separated Gaussians

Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman

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

5 Scopus citations

Abstract

Learning the parameters of Gaussian mixture models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian mixture model subject to the strong constraint of differential privacy. In particular, we give a differentially private analogue of the algorithm of Achlioptas and McSherry. Our algorithm has two key properties not achieved by prior work: (1) The algorithm's sample complexity matches that of the corresponding non-private algorithm up to lower order terms in a wide range of parameters. (2) The algorithm does not require strong a priori bounds on the parameters of the mixture components.

Original languageEnglish
Title of host publication2020 Information Theory and Applications Workshop, ITA 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728141909
DOIs
StatePublished - 2 Feb 2020
Event2020 Information Theory and Applications Workshop, ITA 2020 - San Diego, United States
Duration: 2 Feb 20207 Feb 2020

Publication series

Name2020 Information Theory and Applications Workshop, ITA 2020

Conference

Conference2020 Information Theory and Applications Workshop, ITA 2020
Country/TerritoryUnited States
CitySan Diego
Period2/02/207/02/20

Bibliographical note

Publisher Copyright:
© 2020 IEEE.

Funding

Part of this work was done while the authors were visiting the Simons Institute for Theoretical Computer Science. Parts of this work were done while GK was supported as a Microsoft Research Fellow, as part of the Simons-Berkeley Research Fellowship program, while visiting Microsoft Research, Redmond, and while supported by a University of Waterloo startup grant. This work was done while OS was affiliated with the University of Alberta. OS gratefully acknowledges the Natural Sciences and Engineering Research Council of Canada (NSERC) for its support through grant #2017-06701. JU and VS were supported by NSF grants CCF-1718088, CCF-1750640, and CNS-1816028.

FundersFunder number
National Science FoundationCCF-1750640, CNS-1816028, CCF-1718088
Microsoft Research
Natural Sciences and Engineering Research Council of Canada2017-06701
University of Waterloo

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