Sample-Efficient Private Learning of Mixtures of Gaussians

Learning Gaussian Mixture Models (GMMs) is a core problem in machine learning with numerous applications. However, learning GMMs with limited data while preserving data privacy is particularly challenging. Existing methods often require an excessively large number of data samples or fail to provide optimal theoretical guarantees regarding the necessary number of samples. This results in algorithms that are computationally inefficient or impractical for real-world applications. Prior work lacked optimal bounds on the number of samples required, especially when the dimension of the data is high.

This work addresses these limitations by providing improved sample complexity bounds for privately learning GMMs. The researchers present novel algorithms that significantly reduce the number of samples required compared to existing methods. These improvements are particularly noteworthy in high-dimensional settings and for learning mixtures of univariate Gaussians. Their theoretical analysis demonstrates the optimality of their bounds in certain scenarios, offering a new level of efficiency and accuracy in privacy-preserving machine learning.