Differentially Private Numerical Vector Analyses in the Local and Shuffle Model. (arXiv:2304.04410v1 [cs.CR])

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
$O(\frac{ds}{n\epsilon^2})$, where $d$ represents the dimension of the
numerical vector and $s$ denotes the number of non-zero entries. By converting
the conditional/unconditional numerical mean estimation problem into a
frequency estimation problem, we develop an optimal and efficient mechanism
called Collision. …

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