Lightweight Protocols for Distributed Private Quantile Estimation
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910814861000704 |
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| author | Aamand, Anders Boninsegna, Fabrizio Gentle, Abigail Imola, Jacob Pagh, Rasmus |
| author_facet | Aamand, Anders Boninsegna, Fabrizio Gentle, Abigail Imola, Jacob Pagh, Rasmus |
| contents | Distributed data analysis is a large and growing field driven by a massive proliferation of user devices, and by privacy concerns surrounding the centralised storage of data. We consider two \emph{adaptive} algorithms for estimating one quantile (e.g.~the median) when each user holds a single data point lying in a domain $[B]$ that can be queried once through a private mechanism; one under local differential privacy (LDP) and another for shuffle differential privacy (shuffle-DP). In the adaptive setting we present an $\varepsilon$-LDP algorithm which can estimate any quantile within error $α$ only requiring $O(\frac{\log B}{\varepsilon^2α^2})$ users, and an $(\varepsilon,δ)$-shuffle DP algorithm requiring only $\widetilde{O}((\frac{1}{\varepsilon^2}+\frac{1}{α^2})\log B)$ users. Prior (nonadaptive) algorithms require more users by several logarithmic factors in $B$. We further provide a matching lower bound for adaptive protocols, showing that our LDP algorithm is optimal in the low-$\varepsilon$ regime. Additionally, we establish lower bounds against non-adaptive protocols which paired with our understanding of the adaptive case, proves a fundamental separation between these models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02990 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lightweight Protocols for Distributed Private Quantile Estimation Aamand, Anders Boninsegna, Fabrizio Gentle, Abigail Imola, Jacob Pagh, Rasmus Cryptography and Security Distributed data analysis is a large and growing field driven by a massive proliferation of user devices, and by privacy concerns surrounding the centralised storage of data. We consider two \emph{adaptive} algorithms for estimating one quantile (e.g.~the median) when each user holds a single data point lying in a domain $[B]$ that can be queried once through a private mechanism; one under local differential privacy (LDP) and another for shuffle differential privacy (shuffle-DP). In the adaptive setting we present an $\varepsilon$-LDP algorithm which can estimate any quantile within error $α$ only requiring $O(\frac{\log B}{\varepsilon^2α^2})$ users, and an $(\varepsilon,δ)$-shuffle DP algorithm requiring only $\widetilde{O}((\frac{1}{\varepsilon^2}+\frac{1}{α^2})\log B)$ users. Prior (nonadaptive) algorithms require more users by several logarithmic factors in $B$. We further provide a matching lower bound for adaptive protocols, showing that our LDP algorithm is optimal in the low-$\varepsilon$ regime. Additionally, we establish lower bounds against non-adaptive protocols which paired with our understanding of the adaptive case, proves a fundamental separation between these models. |
| title | Lightweight Protocols for Distributed Private Quantile Estimation |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2502.02990 |