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Smooth Sensitivity Revisited: Towards Optimality

Authors Richard Hladík , Jakub Tětek

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  • Security and privacy → Privacy-preserving protocols
Keywords
  • differential privacy
  • smooth sensitivity

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Abstract

Smooth sensitivity is one of the most commonly used techniques for designing practical differentially private mechanisms. In this approach, one computes the smooth sensitivity of a given query q on the given input D and releases q(D) with noise added proportional to this smooth sensitivity. One question remains: what distribution should we pick the noise from? 
In this paper, we give a new class of distributions suitable for the use with smooth sensitivity, which we name the PolyPlace distribution. This distribution improves upon the state-of-the-art Student’s T distribution in terms of standard deviation by arbitrarily large factors, depending on a "smoothness parameter" γ, which one has to set in the smooth sensitivity framework. Moreover, our distribution is defined for a wider range of parameter γ, which can lead to significantly better performance. 
Furthermore, we prove that the PolyPlace distribution converges for γ → 0 to the Laplace distribution and so does its variance. This means that the Laplace mechanism is a limit special case of the PolyPlace mechanism. This implies that our mechanism is in a certain sense optimal for γ → 0.

Cite As Get BibTex

Richard Hladík and Jakub Tětek. Smooth Sensitivity Revisited: Towards Optimality. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FORC.2025.2

Author Details

Richard Hladík
  • ETH Zurich, Switzerland
Jakub Tětek
  • INSAIT, Sofia University "St. Kliment Ohridski", Bulgaria

Funding

Partially funded by the Ministry of Education and Science of Bulgaria’s support for INSAIT as part of the Bulgarian National Roadmap for Research Infrastructure. Partially supported by the VILLUM Foundation grants 54451 and 16582.
  • Hladík, Richard: Supported in part by the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement No. 949272)

Acknowledgements

We would like to thank Rasmus Pagh and Adam Sealfon for helpful discussions. We would like to thank Rasmus Pagh for hosting Richard at the University of Copenhagen. Jakub worked on this paper while affiliated with BARC, University of Copenhagen. Richard partially worked on this paper while visiting BARC, University of Copenhagen.

References

  1. Hilal Asi and John C. Duchi. Instance-optimality in differential privacy via approximate inverse sensitivity mechanisms. In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, volume 33, pages 14106-14117, 2020. URL: https://proceedings.neurips.cc/paper/2020/hash/a267f936e54d7c10a2bb70dbe6ad7a89-Abstract.html.
  2. Hilal Asi and John C. Duchi. Near instance-optimality in differential privacy. CoRR, abs/2005.10630, 2020. URL: https://doi.org/10.48550/arXiv.2005.10630.
  3. Mark Bun and Thomas Steinke. Average-case averages: Private algorithms for smooth sensitivity and mean estimation. In Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, volume 32, pages 181-191, 2019. URL: https://proceedings.neurips.cc/paper/2019/hash/3ef815416f775098fe977004015c6193-Abstract.html.
  4. Cynthia Dwork and Jing Lei. Differential privacy and robust statistics. In Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, Bethesda, MD, USA, May 31 - June 2, 2009, pages 371-380. ACM, 2009. URL: https://doi.org/10.1145/1536414.1536466.
  5. Cynthia Dwork and Aaron Roth. The algorithmic foundations of differential privacy. Foundations and Trends® in Theoretical Computer Science, 9(3-4):211-407, 2014. URL: https://doi.org/10.1561/0400000042.
  6. Cynthia Dwork and Guy N. Rothblum. Concentrated differential privacy. CoRR, abs/1603.01887, 2016. URL: https://doi.org/10.48550/arXiv.1603.01887.
  7. Juanru Fang, Wei Dong, and Ke Yi. Shifted inverse: A general mechanism for monotonic functions under user differential privacy. In Proceedings of the 2022 ACM SIGSAC Conference on Computer and Communications Security, CCS 2022, Los Angeles, CA, USA, November 7-11, 2022, pages 1009-1022. ACM, 2022. URL: https://doi.org/10.1145/3548606.3560567.
  8. Natasha Fernandes, Annabelle McIver, and Carroll Morgan. The Laplace mechanism has optimal utility for differential privacy over continuous queries. In 36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021, Rome, Italy, June 29 - July 2, 2021, pages 1-12. IEEE, IEEE, 2021. URL: https://doi.org/10.1109/LICS52264.2021.9470718.
  9. Alon Gonem and Ran Gilad-Bachrach. Smooth sensitivity based approach for differentially private PCA. In Algorithmic Learning Theory, ALT 2018, 7-9 April 2018, Lanzarote, Canary Islands, Spain, volume 83 of Proceedings of Machine Learning Research, pages 438-450. PMLR, PMLR, 2018. URL: http://proceedings.mlr.press/v83/gonem18a.html.
  10. Jesse Laeuchli, Yunior Ramírez-Cruz, and Rolando Trujillo-Rasua. Analysis of centrality measures under differential privacy models. Applied Mathematics and Computation, 412:126546, 2022. URL: https://doi.org/10.1016/j.amc.2021.126546.
  11. Mingzhu Li and Xuebin Ma. Bayesian networks-based data publishing method using smooth sensitivity. In IEEE International Conference on Parallel & Distributed Processing with Applications, Ubiquitous Computing & Communications, Big Data & Cloud Computing, Social Computing & Networking, Sustainable Computing & Communications, ISPA/IUCC/BDCloud/SocialCom/SustainCom 2018, Melbourne, Australia, December 11-13, 2018, pages 795-800. IEEE, IEEE, 2018. URL: https://doi.org/10.1109/BDCloud.2018.00119.
  12. Kobbi Nissim, Sofya Raskhodnikova, and Adam D. Smith. Smooth sensitivity and sampling in private data analysis. In Proceedings of the 39th Annual ACM Symposium on Theory of Computing, San Diego, California, USA, June 11-13, 2007, pages 75-84. ACM, 2007. URL: https://doi.org/10.1145/1250790.1250803.
  13. Lichao Sun, Yingbo Zhou, Philip S. Yu, and Caiming Xiong. Differentially private deep learning with smooth sensitivity. CoRR, abs/2003.00505, 2020. URL: https://doi.org/10.48550/arXiv.2003.00505.
  14. Salil P. Vadhan. The complexity of differential privacy. In Tutorials on the Foundations of Cryptography, pages 347-450. Springer International Publishing, 2017. URL: https://doi.org/10.1007/978-3-319-57048-8_7.
  15. Yue Wang and Xintao Wu. Preserving differential privacy in degree-correlation based graph generation. Trans. Data Priv., 6(2):127-145, 2013. URL: http://www.tdp.cat/issues11/abs.a113a12.php.
  16. Bangzhou Xin, Wei Yang, Shaowei Wang, and Liusheng Huang. Differentially private greedy decision forest. In IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2019, Brighton, United Kingdom, May 12-17, 2019, pages 2672-2676. IEEE, IEEE, 2019. URL: https://doi.org/10.1109/ICASSP.2019.8682219.
  17. Akito Yamamoto and Tetsuo Shibuya. Privacy-preserving publication of GWAS statistics using smooth sensitivity. In 20th Annual International Conference on Privacy, Security and Trust, PST 2023, Copenhagen, Denmark, August 21-23, 2023, pages 1-12. IEEE, IEEE, 2023. URL: https://doi.org/10.1109/PST58708.2023.10320160.
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