Locally Private Gaussian Estimation

Abstract

We study a basic private estimation problem: each of $n$ users draws a single i.i.d. sample from an unknown Gaussian distribution, and the goal is to estimate the mean of this Gaussian distribution while satisfying local differential privacy for each user. Informally, local differential privacy requires that each data point is individually and independently privatized before it is passed to a learning algorithm. Locally private Gaussian estimation is therefore difficult because the data domain is unbounded: users may draw arbitrarily different inputs, but local differential privacy nonetheless mandates that different users have (worst-case) similar privatized output distributions. We provide both adaptive two-round solutions and nonadaptive one-round solutions for locally private Gaussian estimation. We then partially match these upper bounds with an information-theoretic lower bound. This lower bound shows that our accuracy guarantees are tight up to logarithmic factors for all sequentially interactive $(\epsilon ,\delta )$-locally private protocols.

References in corpus (5)

• Lower Bounds for Locally Private Estimation via Communication Complexity
• Privately Learning High-Dimensional Distributions
• Tight Lower Bounds for Locally Differentially Private Selection
• Locally Private Mean Estimation: Z-test and Tight Confidence Intervals
• Local Private Hypothesis Testing: Chi-Square Tests

Cited by in corpus (6)

• Lower Bounds for Locally Private Estimation via Communication Complexity
• Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation
• Covariance-Aware Private Mean Estimation Without Private Covariance Estimation
• Locally Differentially Private Analysis of Graph Statistics
• Private Identity Testing for High-Dimensional Distributions
• Locally Differentially Private Data Collection and Analysis