Personalized Heterogeneous Mean Estimation Under User-Level LDP

We study personalized heterogeneous mean estimation under user-level local differential privacy (LDP), which protects the privacy of local datasets with multiple samples. We consider a distributed environment with $n$ users, each associated with one of $k$ clusters. Our goal is to estimate the mean of each cluster while preserving the privacy of users' local datasets. Focusing on the scalar case, we propose algorithms that handle scenarios with (unknown) equal and unequal variance proxies (spans of the clusters), and even the number of clusters. Our methods identify the clusters via private frequency estimation and subsequently perform private mean estimation for each cluster. Theoretical guarantees on the trade-off between user-level local differential privacy guarantees and performance are provided.