Differentially Private Algorithms for Learning Mixtures of Separated Gaussians
This work addresses privacy-preserving data analysis for machine learning practitioners, offering a differentially private solution with minimal performance loss compared to non-private methods.
The authors tackled the problem of learning parameters of high-dimensional, well-separated Gaussian mixture models under differential privacy constraints, developing an algorithm that matches non-private sample complexity up to lower-order terms and eliminates the need for strong prior bounds on mixture components.
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.