Locally Private Gaussian Estimation
This work addresses the challenge of private statistical estimation for users in scenarios where data is sensitive and unbounded, offering tight theoretical bounds, though it is incremental in the context of local privacy research.
The paper tackles the problem of estimating the mean of a Gaussian distribution from user samples while ensuring local differential privacy, which is challenging due to the unbounded data domain. It provides adaptive two-round and nonadaptive one-round solutions with accuracy guarantees that are shown to be tight up to logarithmic factors for all sequentially interactive protocols.
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 $(\varepsilon,δ)$-locally private protocols.