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arXiv · 1909.03951

Differentially Private Algorithms for Learning Mixtures of Separated Gaussians

Gautam Kamath·Or Sheffet·Vikrant Singhal·Jonathan Ullman
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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.

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Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman. 2019-09-09. Differentially Private Algorithms for Learning Mixtures of Separated Gaussians. https://arxiv.org/abs/1909.03951

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