CoinPress: Practical Private Mean and Covariance Estimation

Understand

We present simple differentially private estimators for the mean and covariance of multivariate sub-Gaussian data that are accurate at small sample sizes.

• We demonstrate the effectiveness of our algorithms both theoretically and empirically using synthetic and real-world datasets -- showing that their asymptotic error rates match the state-of-the-art theoretical bounds, and that they concretely outperform all previous methods.
• Specifically, previous estimators either have weak empirical accuracy at small sample sizes, perform poorly for multivariate data, or require the user to provide strong a priori estimates for the parameters.