Distribution-Aware Mean Estimation under User-level Local Differential Privacy
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909346845163520 |
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| author | Pla, Corentin Richard, Hugo Vono, Maxime |
| author_facet | Pla, Corentin Richard, Hugo Vono, Maxime |
| contents | 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 $μ$; $m_u$ 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 $μ$ 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 $u$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distribution-Aware Mean Estimation under User-level Local Differential Privacy Pla, Corentin Richard, Hugo Vono, Maxime Methodology Artificial Intelligence Cryptography and Security Machine Learning 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 $μ$; $m_u$ 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 $μ$ 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 $u$. |
| title | Distribution-Aware Mean Estimation under User-level Local Differential Privacy |
| topic | Methodology Artificial Intelligence Cryptography and Security Machine Learning |
| url | https://arxiv.org/abs/2410.09506 |