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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2411.08791 |
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| _version_ | 1866908345139462144 |
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| author | Zamanlooy, Behnoosh Diaz, Mario Asoodeh, Shahab |
| author_facet | Zamanlooy, Behnoosh Diaz, Mario Asoodeh, Shahab |
| contents | Local differential privacy (LDP) is increasingly employed in privacy-preserving machine learning to protect user data before sharing it with an untrusted aggregator. Most LDP methods assume that users possess only a single data record, which is a significant limitation since users often gather extensive datasets (e.g., images, text, time-series data) and frequently have access to public datasets. To address this limitation, we propose a locally private sampling framework that leverages both the private and public datasets of each user. Specifically, we assume each user has two distributions: $p$ and $q$ that represent their private dataset and the public dataset, respectively. The objective is to design a mechanism that generates a private sample approximating $p$ while simultaneously preserving $q$. We frame this objective as a minimax optimization problem using $f$-divergence as the utility measure. We fully characterize the minimax optimal mechanisms for general $f$-divergences provided that $p$ and $q$ are discrete distributions. Remarkably, we demonstrate that this optimal mechanism is universal across all $f$-divergences. Experiments validate the effectiveness of our minimax optimal sampler compared to the state-of-the-art locally private sampler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Locally Private Sampling with Public Data Zamanlooy, Behnoosh Diaz, Mario Asoodeh, Shahab Machine Learning Local differential privacy (LDP) is increasingly employed in privacy-preserving machine learning to protect user data before sharing it with an untrusted aggregator. Most LDP methods assume that users possess only a single data record, which is a significant limitation since users often gather extensive datasets (e.g., images, text, time-series data) and frequently have access to public datasets. To address this limitation, we propose a locally private sampling framework that leverages both the private and public datasets of each user. Specifically, we assume each user has two distributions: $p$ and $q$ that represent their private dataset and the public dataset, respectively. The objective is to design a mechanism that generates a private sample approximating $p$ while simultaneously preserving $q$. We frame this objective as a minimax optimization problem using $f$-divergence as the utility measure. We fully characterize the minimax optimal mechanisms for general $f$-divergences provided that $p$ and $q$ are discrete distributions. Remarkably, we demonstrate that this optimal mechanism is universal across all $f$-divergences. Experiments validate the effectiveness of our minimax optimal sampler compared to the state-of-the-art locally private sampler. |
| title | Locally Private Sampling with Public Data |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2411.08791 |