Differentially Private Algorithms for Learning Mixtures of Separated Gaussians
By Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman. 2019
51 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence
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In Artificial Intelligence
- Yatharth Dubey
- Aleksandra Korolova
- Krishnaram Kenthapadi
- Jayadev Acharya
- Rasmus Pagh
- Thanh T. L. Tran
- Ziteng Sun
- Ninghui Li
Citations in the corpus
- The Power of the Hybrid Model for Mean Estimation (2018, background): “However, DP mean estimation of distributions under both the TCM and LM has been studied since the models’ introductions [17, 21, 56], and continues to be actively studied to this day [2, 15, 18, 20, 22, 28, 29, 32, 37, 39–42].”
- Private Mean Estimation of Heavy-Tailed Distributions (2020, unknown): “Privately learning mixtures of Gaussians was considered in [NRS07, KSSU19].”