Differentially Private Numerical Vector Analyses in the Local and Shuffle Model

Numerical vector aggregation plays a crucial role in privacy-sensitive applications, such as distributed gradient estimation in federated learning and statistical analysis of key-value data. In the context of local differential privacy, this study provides a tight minimax error bound of $O(\frac{ds}{nε^2})$, where $d$ represents the dimension of the numerical vector and $s$ denotes the number o…