CoinPress: Practical Private Mean and Covariance Estimation

NeurIPS 2020 · Sourav Biswas, Yihe Dong, Gautam Kamath, Jonathan Ullman ·

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.