%0 Journal Article %1 kamath2019differentially %A Kamath, Gautam %A Sheffet, Or %A Singhal, Vikrant %A Ullman, Jonathan %D 2019 %K differential-privacy generative-models %T Differentially Private Algorithms for Learning Mixtures of Separated Gaussians %U http://arxiv.org/abs/1909.03951 %X Learning the parameters of a Gaussian mixtures 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.

@article{kamath2019differentially, abstract = {Learning the parameters of a Gaussian mixtures 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.}, added-at = {2019-09-11T01:19:18.000+0200}, author = {Kamath, Gautam and Sheffet, Or and Singhal, Vikrant and Ullman, Jonathan}, biburl = {https://www.bibsonomy.org/bibtex/214f2aad9b3442e232dbdfc979956e628/kirk86}, description = {[1909.03951] Differentially Private Algorithms for Learning Mixtures of Separated Gaussians}, interhash = {a9294fa4b4b50a3be60ab86c54398aac}, intrahash = {14f2aad9b3442e232dbdfc979956e628}, keywords = {differential-privacy generative-models}, note = {cite arxiv:1909.03951Comment: To appear in NeurIPS 2019}, timestamp = {2019-09-11T01:19:18.000+0200}, title = {Differentially Private Algorithms for Learning Mixtures of Separated Gaussians}, url = {http://arxiv.org/abs/1909.03951}, year = 2019 }