Given samples from a distribution, can we estimate its mean and covariance? Absent privacy considerations, the empirical estimates generally suffice. However, under the constraint of differential privacy, the picture changes dramatically. I will discuss a number of new challenges that arise in this setting, and the solutions we propose to address them. Some qualitative differences (with respect to the non-private setting) that we investigate include a dependence on the range of the data, improved rates with stronger moment bounds, and novel estimation techniques for multivariate settings.
Based on joint works with Sourav Biswas, Yihe Dong, Jerry Li, Vikrant Singhal, and Jonathan Ullman.