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Differentially Private Algorithms for Learning Mixtures of Separated Gaussians
Gautam Kamath · Or Sheffet · Vikrant Singhal · Jonathan Ullman

Tue Dec 10 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #94

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 requires very weak a priori bounds on the parameters of the mixture components.

Author Information

Gautam Kamath (University of Waterloo)
Or Sheffet (University of Alberta)
Vikrant Singhal (Northeastern University)
Jonathan Ullman (Northeastern University)

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