Distribution-Aware Mean Estimation under User-level Local Differential Privacy

• URL: http://arxiv.org/abs/2410.09506v1
• Date: Sat, 12 Oct 2024 11:57:52 GMT
• Title: Distribution-Aware Mean Estimation under User-level Local Differential Privacy
• Authors: Corentin Pla, Hugo Richard, Maxime Vono,
• Abstract summary: We consider the problem of mean estimation under user-level local differential privacy, where $n$ users are contributing through their local pool of data samples. Based on a distribution-aware mean estimation algorithm, we establish an $M$-dependent upper bounds on the worst-case risk over $mu$ for the task of mean estimation.
• Score: 5.267844649650687
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the problem of mean estimation under user-level local differential privacy, where $n$ users are contributing through their local pool of data samples. Previous work assume that the number of data samples is the same across users. In contrast, we consider a more general and realistic scenario where each user $u \in [n]$ owns $m_u$ data samples drawn from some generative distribution $\mu$; $m_u$ being unknown to the statistician but drawn from a known distribution $M$ over $\mathbb{N}^\star$. Based on a distribution-aware mean estimation algorithm, we establish an $M$-dependent upper bounds on the worst-case risk over $\mu$ for the task of mean estimation. We then derive a lower bound. The two bounds are asymptotically matching up to logarithmic factors and reduce to known bounds when $m_u = m$ for any user $u$.

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