Private Learning of Gaussians and Their Mixtures

Explore the intricacies of private learning for Gaussian distributions and their mixtures in this 30-minute talk by Hassan Ashtiani from McMaster University. Delve into topics such as PAC learning of distributions, univariate Gaussians, robustness, and private hypothesis selection. Examine the challenges of high-dimensional Gaussians and covariance estimation in the context of differential privacy. Gain insights into stable histogram methods and the complexities of privately learning general Gaussians. Part of the "Workshop on Differential Privacy and Statistical Data Analysis" at the Fields Institute, this lecture offers a comprehensive overview of current research in private statistical learning.

Intro
PAC Learning of Distributions
Learning Univariate Gaussians
Robustness?
Choosing from two distributions
Private Hypothesis Selection
Stable Histogram Bun, Nissim, Stemmerid
Univariate Gaussians Karwa, Vadhan'17
Univariate GMMS
High-dimensional Gaussians
Private Learning of General Gaussian
Privately Learning Gaussians
Case of covariance estimation
Final Thoughts . In many cases our robust methods have large C