Differentially Private Algorithms for Learning Mixtures of Separated Gaussians

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

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Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman


<p>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.</p>