2020/06/11 by Sourav Biswas, Yihe Dong, Biswas, Sourav +5 · 4 citations
Computer Science · Mathematics · #Cryptography and Security (cs.CR) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Privacy-Preserving Technologies in Data #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2006.06618
openalex publication_date 2020/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.