CoinPress: Practical Private Mean and Covariance Estimation
This work addresses the need for practical, accurate private statistical estimation for data analysts, offering improvements over existing methods that often fail with small samples or require strong prior parameter estimates.
The authors tackled the problem of estimating the mean and covariance of multivariate sub-Gaussian data under differential privacy constraints, achieving state-of-the-art theoretical bounds and outperforming previous methods in accuracy at small sample sizes.
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.