Differentially Private Algorithms for Learning Mixtures of Separated Gaussians

Gautam Kamath; Or Sheffet; Vikrant Singhal; Jonathan Ullman

doi:10.1109/ITA50056.2020.9244945

Differentially Private Algorithms for Learning Mixtures of Separated Gaussians

Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 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 language	English
Title of host publication	2020 Information Theory and Applications Workshop, ITA 2020
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781728141909
DOIs	https://doi.org/10.1109/ITA50056.2020.9244945
State	Published - 2 Feb 2020
Event	2020 Information Theory and Applications Workshop, ITA 2020 - San Diego, United States Duration: 2 Feb 2020 → 7 Feb 2020

Publication series

Name	2020 Information Theory and Applications Workshop, ITA 2020

Conference

Conference	2020 Information Theory and Applications Workshop, ITA 2020
Country/Territory	United States
City	San Diego
Period	2/02/20 → 7/02/20

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.

Funders	Funder number
National Science Foundation	CCF-1750640, CNS-1816028, CCF-1718088
Microsoft Research
Natural Sciences and Engineering Research Council of Canada	2017-06701
University of Waterloo

Access to Document

10.1109/ITA50056.2020.9244945

Cite this

Kamath, G., Sheffet, O., Singhal, V., & Ullman, J. (2020). Differentially Private Algorithms for Learning Mixtures of Separated Gaussians. In 2020 Information Theory and Applications Workshop, ITA 2020 Article 9244945 (2020 Information Theory and Applications Workshop, ITA 2020). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITA50056.2020.9244945

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Kamath, G, Sheffet, O, Singhal, V & Ullman, J 2020, Differentially Private Algorithms for Learning Mixtures of Separated Gaussians. in 2020 Information Theory and Applications Workshop, ITA 2020., 9244945, 2020 Information Theory and Applications Workshop, ITA 2020, Institute of Electrical and Electronics Engineers Inc., 2020 Information Theory and Applications Workshop, ITA 2020, San Diego, United States, 2/02/20. https://doi.org/10.1109/ITA50056.2020.9244945

Differentially Private Algorithms for Learning Mixtures of Separated Gaussians. / Kamath, Gautam; Sheffet, Or; Singhal, Vikrant et al.
2020 Information Theory and Applications Workshop, ITA 2020. Institute of Electrical and Electronics Engineers Inc., 2020. 9244945 (2020 Information Theory and Applications Workshop, ITA 2020).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Differentially Private Algorithms for Learning Mixtures of Separated Gaussians

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