2024/02/11 by Karan N. Chadha, John C. Duchi, Chadha, Karan +3 · 1 citation
Mathematics · Medicine · #Cryptography and Security (cs.CR) #Data-Driven Disease Surveillance #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2402.07131
openalex publication_date 2024/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the task of constructing confidence intervals with differential privacy. We propose two private variants of the non-parametric bootstrap, which privately compute the median of the results of multiple "little" bootstraps run on partitions of the data and give asymptotic bounds on the coverage error of the resulting confidence intervals. For a fixed differential privacy parameter ε, our methods enjoy the same error rates as that of the non-private bootstrap to within logarithmic factors in the sample size n. We empirically validate the performance of our methods for mean estimation, median estimation, and logistic regression with both real and synthetic data. Our methods achieve similar coverage accuracy to existing methods (and non-private baselines) while providing notably shorter (\gtrsim 10 times) confidence intervals than previous approaches.