Locally Private Gaussian Estimation

Understand

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.