Differentially private algorithms for learning mixtures of separated gaussians

Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman

Research output: Contribution to journalConference articlepeer-review

22 Scopus citations


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 (COLT 2005). 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 requires very weak a priori bounds on the parameters of the mixture.

Original languageEnglish
JournalAdvances in Neural Information Processing Systems
StatePublished - 2019
Event33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019 - Vancouver, Canada
Duration: 8 Dec 201914 Dec 2019

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© 2019 Neural information processing systems foundation. All rights reserved.


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