CoinPress: Practical Private Mean and Covariance Estimation

TL;DR

This paper introduces practical differentially private estimators for mean and covariance of multivariate sub-Gaussian data, achieving high accuracy with small samples and outperforming previous methods both theoretically and empirically.

Contribution

The paper proposes simple, effective private estimators for mean and covariance that work well with small samples and do not require strong prior parameter estimates.

Findings

Estimators match state-of-the-art asymptotic error bounds.

Algorithms outperform previous methods in empirical tests.

Effective for multivariate sub-Gaussian data at small sample sizes.

Abstract

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.