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

Fuente: arXiv
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Main Authors: Pla, Corentin, Richard, Hugo, Vono, Maxime
Format: Preprint
Published: 2024
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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