Locally Private Sampling with Public Data

Behnoosh Zamanlooy, Mario Diaz, Shahab Asoodeh
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:622-630, 2025.

Abstract

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 and public datasets, 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 mechanism compared to the state-of-the-art private sampler.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-zamanlooy25a, title = {Locally Private Sampling with Public Data}, author = {Zamanlooy, Behnoosh and Diaz, Mario and Asoodeh, Shahab}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {622--630}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/zamanlooy25a/zamanlooy25a.pdf}, url = {https://proceedings.mlr.press/v258/zamanlooy25a.html}, abstract = {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 and public datasets, 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 mechanism compared to the state-of-the-art private sampler.} }
Endnote
%0 Conference Paper %T Locally Private Sampling with Public Data %A Behnoosh Zamanlooy %A Mario Diaz %A Shahab Asoodeh %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-zamanlooy25a %I PMLR %P 622--630 %U https://proceedings.mlr.press/v258/zamanlooy25a.html %V 258 %X 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 and public datasets, 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 mechanism compared to the state-of-the-art private sampler.
APA
Zamanlooy, B., Diaz, M. & Asoodeh, S.. (2025). Locally Private Sampling with Public Data. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:622-630 Available from https://proceedings.mlr.press/v258/zamanlooy25a.html.

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