CoinPress: Practical Private Mean and Covariance Estimation

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.

Code is available at https://github.com/twistedcubic/coin-press. Experimental results were inadvertently commented out of previous version

References in corpus (8)

• Collecting Telemetry Data Privately
• The Noisy Power Method: A Meta Algorithm with Applications
• The Cost of Privacy: Rates of Convergence for Parameter Estimation with Differential Privacy
• Privately Learning High-Dimensional Distributions
• Differentially Private Confidence Intervals
• A Primer on Private Statistics
• Differentially Private Assouad, Fano, and Le Cam
• Privately Learning Markov Random Fields

Cited by in corpus (9)

• The Cost of Privacy: Rates of Convergence for Parameter Estimation with Differential Privacy
• Private Mean Estimation of Heavy-Tailed Distributions
• Enabling Fast Differentially Private SGD via Just-in-Time Compilation and Vectorization
• Robust and Differentially Private Mean Estimation
• On the Sample Complexity of Privately Learning Unbounded High-Dimensional Gaussians
• Differential privacy and robust statistics in high dimensions
• Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacy
• Privately Learning Mixtures of Axis-Aligned Gaussians
• Selective MPC: Distributed Computation of Differentially Private Key-Value Statistics