Better Gaussian Mechanism using Correlated Noise
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910881227472896 |
|---|---|
| author | Lebeda, Christian Janos |
| author_facet | Lebeda, Christian Janos |
| contents | We present a simple variant of the Gaussian mechanism for answering differentially private queries when the sensitivity space has a certain common structure. Our motivating problem is the fundamental task of answering $d$ counting queries under the add/remove neighboring relation. The standard Gaussian mechanism solves this task by adding noise distributed as a Gaussian with variance scaled by $d$ independently to each count. We show that adding a random variable distributed as a Gaussian with variance scaled by $(\sqrt{d} + 1)/4$ to all counts allows us to reduce the variance of the independent Gaussian noise samples to scale only with $(d + \sqrt{d})/4$. The total noise added to each counting query follows a Gaussian distribution with standard deviation scaled by $(\sqrt{d} + 1)/2$ rather than $\sqrt{d}$. The central idea of our mechanism is simple and the technique is flexible. We show that applying our technique to another problem gives similar improvements over the standard Gaussian mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Better Gaussian Mechanism using Correlated Noise Lebeda, Christian Janos Cryptography and Security Data Structures and Algorithms We present a simple variant of the Gaussian mechanism for answering differentially private queries when the sensitivity space has a certain common structure. Our motivating problem is the fundamental task of answering $d$ counting queries under the add/remove neighboring relation. The standard Gaussian mechanism solves this task by adding noise distributed as a Gaussian with variance scaled by $d$ independently to each count. We show that adding a random variable distributed as a Gaussian with variance scaled by $(\sqrt{d} + 1)/4$ to all counts allows us to reduce the variance of the independent Gaussian noise samples to scale only with $(d + \sqrt{d})/4$. The total noise added to each counting query follows a Gaussian distribution with standard deviation scaled by $(\sqrt{d} + 1)/2$ rather than $\sqrt{d}$. The central idea of our mechanism is simple and the technique is flexible. We show that applying our technique to another problem gives similar improvements over the standard Gaussian mechanism. |
| title | Better Gaussian Mechanism using Correlated Noise |
| topic | Cryptography and Security Data Structures and Algorithms |
| url | https://arxiv.org/abs/2408.06853 |