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Uniformity Testing Under User-Level Local Privacy

Authors Clément L. Canonne , Abigail Gentle , Vikrant Singhal

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Subject Classification

ACM Subject Classification
  • Security and privacy
  • Security and privacy → Usability in security and privacy
  • Security and privacy → Privacy protections
  • Theory of computation → Theory of database privacy and security
  • Mathematics of computing → Hypothesis testing and confidence interval computation
Keywords
  • Differential Privacy
  • Local Differential Privacy
  • Uniformity Testing
  • Identity Testing
  • Hypothesis Testing
  • User-Level Differential Privacy
  • Person-Level Differential Privacy

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Abstract

We initiate the study of distribution testing under user-level local differential privacy, where each of n users contributes m samples from the unknown underlying distribution. This setting, albeit very natural, is significantly more challenging than the usual locally private setting, as for the same parameter ε the privacy guarantee must now apply to a full batch of m data points. While some recent work considers distribution learning in this user-level setting, nothing was known for even the most fundamental testing task, uniformity testing (and its generalization, identity testing).
We address this gap, by providing (nearly) sample-optimal user-level LDP algorithms for uniformity and identity testing. Motivated by practical considerations, our main focus is on the private-coin, symmetric setting, which does not require users to share a common random seed nor to have been assigned a globally unique identifier.

Cite As Get BibTex

Clément L. Canonne, Abigail Gentle, and Vikrant Singhal. Uniformity Testing Under User-Level Local Privacy. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.33

Author Details

Clément L. Canonne
  • The University of Sydney, Australia
Abigail Gentle
  • The University of Sydney, Australia
Vikrant Singhal
  • Harvard University, Cambridge, MA, USA

Funding

  • Canonne, Clément L.: Supported by an ARC DECRA (DE230101329).
  • Gentle, Abigail: Supported by an Australian Government Research Training Program (RTP) Scholarship.
  • Singhal, Vikrant: Supported in part by NSF grant BCS-2218803, the D3 Trustworthy AI Lab, and a grant from the Sloan foundation.

References

  1. Jayadev Acharya, Clement Canonne, Cody Freitag, and Himanshu Tyagi. Test without trust: Optimal locally private distribution testing. In Kamalika Chaudhuri and Masashi Sugiyama, editors, Proceedings of Machine Learning Research, volume 89 of Proceedings of Machine Learning Research, pages 2067-2076. PMLR, 16-18 April 2019. URL: http://proceedings.mlr.press/v89/acharya19b.html.
  2. Jayadev Acharya, Clément L. Canonne, Cody Freitag, Ziteng Sun, and Himanshu Tyagi. Inference under information constraints III: local privacy constraints. IEEE J. Sel. Areas Inf. Theory, 2(1):253-267, 2021. URL: https://doi.org/10.1109/JSAIT.2021.3053569.
  3. Jayadev Acharya, Clément L. Canonne, Yuhan Liu, Ziteng Sun, and Himanshu Tyagi. Interactive inference under information constraints. CoRR, abs/2007.10976, 2020. URL: https://arxiv.org/abs/2007.10976.
  4. Jayadev Acharya, Clément L. Canonne, Yuhan Liu, Ziteng Sun, and Himanshu Tyagi. Distributed estimation with multiple samples per user: Sharp rates and phase transition. In Advances in Neural Information Processing Systems 34 (NeurIPS), 2021. Google Scholar
  5. Jayadev Acharya, Clément L. Canonne, and Himanshu Tyagi. Inference under information constraints I: Lower bounds from chi-square contraction. IEEE Trans. Inform. Theory, 66(12):7835-7855, 2020. Preprint available at arXiv:abs/1812.11476. URL: https://doi.org/10.1109/TIT.2020.3028440.
  6. Jayadev Acharya, Clément L. Canonne, and Himanshu Tyagi. Inference under information constraints II: Communication constraints and shared randomness. IEEE Transactions on Information Theory, 2020. In press. Preprint available at arXiv:abs/1804.06952. URL: https://doi.org/10.1109/TIT.2020.3028439.
  7. Jayadev Acharya, Clément L. Canonne, Yanjun Han, Ziteng Sun, and Himanshu Tyagi. Domain compression and its application to randomness-optimal distributed goodness-of-fit. In Jacob Abernethy and Shivani Agarwal, editors, Proceedings of Thirty Third Conference on Learning Theory, volume 125 of Proceedings of Machine Learning Research, pages 3-40. PMLR, 09-12 July 2020. URL: http://proceedings.mlr.press/v125/acharya20a.html.
  8. Jayadev Acharya, Yuhan Liu, and Ziteng Sun. Discrete distribution estimation under user-level local differential privacy. In AISTATS, volume 206 of Proceedings of Machine Learning Research, pages 8561-8585. PMLR, 2023. URL: https://proceedings.mlr.press/v206/acharya23a.html.
  9. Jayadev Acharya and Ziteng Sun. Communication complexity in locally private distribution estimation and heavy hitters. In Kamalika Chaudhuri and Ruslan Salakhutdinov, editors, Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pages 51-60, Long Beach, California, USA, 09-15 June 2019. PMLR. URL: http://proceedings.mlr.press/v97/acharya19c.html.
  10. Jayadev Acharya, Ziteng Sun, and Huanyu Zhang. Differentially private testing of identity and closeness of discrete distributions. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems 31, pages 6878-6891. Curran Associates, Inc., 2018. URL: http://papers.nips.cc/paper/7920-differentially-private-testing-of-identity-and-closeness-of-discrete-distributions.pdf.
  11. Jayadev Acharya, Ziteng Sun, and Huanyu Zhang. Hadamard response: Estimating distributions privately, efficiently, and with little communication. In Kamalika Chaudhuri and Masashi Sugiyama, editors, Proceedings of Machine Learning Research, volume 89 of Proceedings of Machine Learning Research, pages 1120-1129. PMLR, 16-18 April 2019. URL: http://proceedings.mlr.press/v89/acharya19a.html.
  12. Maryam Aliakbarpour, Arnav Burudgunte, Clément L. Canonne, and Ronitt Rubinfeld. Better private distribution testing by leveraging unverified auxiliary data. In COLT, volume 291 of Proceedings of Machine Learning Research, pages 22-63. PMLR, 2025. URL: https://proceedings.mlr.press/v291/aliakbarpour25a.html.
  13. Maryam Aliakbarpour, Ilias Diakonikolas, Daniel Kane, and Ronitt Rubinfeld. Private testing of distributions via sample permutations. In NeurIPS, pages 10877-10888, 2019. URL: https://proceedings.neurips.cc/paper/2019/hash/8e036cc193d0af59aa9b22821248292b-Abstract.html.
  14. Maryam Aliakbarpour, Ilias Diakonikolas, and Ronitt Rubinfeld. Differentially private identity and equivalence testing of discrete distributions. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 169-178, Stockholmsmässan, Stockholm Sweden, 10-15 July 2018. PMLR. URL: http://proceedings.mlr.press/v80/aliakbarpour18a.html.
  15. Kareem Amin, Matthew Joseph, and Jieming Mao. Pan-private uniformity testing. In Jacob Abernethy and Shivani Agarwal, editors, Proceedings of Thirty Third Conference on Learning Theory, volume 125 of Proceedings of Machine Learning Research, pages 183-218. PMLR, 09-12 July 2020. URL: http://proceedings.mlr.press/v125/amin20a.html.
  16. Apple Differential Privacy Team. Learning with Privacy at Scale, 2017. URL: https://machinelearning.apple.com/research/learning-with-privacy-at-scale.
  17. Victor Balcer, Albert Cheu, Matthew Joseph, and Jieming Mao. Connecting robust shuffle privacy and pan-privacy. CoRR, abs/2004.09481, 2020. URL: https://arxiv.org/abs/2004.09481.
  18. Bryan Cai, Constantinos Daskalakis, and Gautam Kamath. Priv'it: Private and sample efficient identity testing. In Proceedings of the 34th International Conference on Machine Learning, ICML '17, pages 635-644. JMLR, Inc., 2017. URL: http://proceedings.mlr.press/v70/cai17a.html.
  19. Clément L. Canonne, Xi Chen, Gautam Kamath, Amit Levi, and Erik Waingarten. Random restrictions of high dimensional distributions and uniformity testing with subcube conditioning. In SODA, pages 321-336. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976465.21.
  20. Clément L. Canonne, Ilias Diakonikolas, Daniel M. Kane, and Alistair Stewart. Testing Bayesian Networks. In Satyen Kale and Ohad Shamir, editors, Proceedings of the 2017 Conference on Learning Theory, volume 65 of Proceedings of Machine Learning Research, pages 370-448, Amsterdam, Netherlands, 07-10 July 2017. PMLR. URL: http://proceedings.mlr.press/v65/canonne17a.html.
  21. Clément L. Canonne, Gautam Kamath, Audra McMillan, Jonathan Ullman, and Lydia Zakynthinou. Private identity testing for high-dimensional distributions. In Advances in Neural Information Processing Systems 33, 2020. To appear. Preprint available at arXiv:abs/1905.11947. Google Scholar
  22. Clément L. Canonne and Hongyi Lyu. Uniformity testing in the shuffle model: Simpler, better, faster. In Karl Bringmann and Timothy M. Chan, editors, 5th Symposium on Simplicity in Algorithms, SOSA@SODA 2022, Virtual Conference, January 10-11, 2022, pages 182-202. SIAM, 2022. URL: https://doi.org/10.1137/1.9781611977066.13.
  23. Clément L. Canonne and Joy Qiping Yang. Simpler distribution testing with little memory. In Merav Parter and Seth Pettie, editors, 2024 Symposium on Simplicity in Algorithms, SOSA 2024, Alexandria, VA, USA, January 8-10, 2024, pages 406-416. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977936.37.
  24. Clément L. Canonne. Topics and techniques in distribution testing: A biased but representative sample. Foundations and Trends® in Communications and Information Theory, 19(6):1032-1198, 2022. URL: https://doi.org/10.1561/0100000114.
  25. Ilias Diakonikolas and Daniel M. Kane. A new approach for testing properties of discrete distributions. In 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016. IEEE Computer Society, 2016. URL: https://doi.org/10.1109/FOCS.2016.78.
  26. Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith. Calibrating noise to sensitivity in private data analysis. In Theory of cryptography, volume 3876 of Lecture Notes in Comput. Sci., pages 265-284. Springer, Berlin, 2006. URL: https://doi.org/10.1007/11681878_14.
  27. Cynthia Dwork and Aaron Roth. The Algorithmic Foundations of Differential Privacy. Foundations and Trends® in Theoretical Computer Science, 9(3-4):211-407, 2013. URL: https://doi.org/10.1561/0400000042.
  28. Cynthia Dwork, Guy N. Rothblum, and Salil Vadhan. Boosting and Differential Privacy. In 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, pages 51-60, 2010. ISSN: 0272-5428. URL: https://doi.org/10.1109/FOCS.2010.12.
  29. Oded Goldreich. The uniform distribution is complete with respect to testing identity to a fixed distribution. Electronic Colloquium on Computational Complexity (ECCC), 23:15, 2016. URL: http://eccc.hpi-web.de/report/2016/015.
  30. Oded Goldreich and Dana Ron. On testing expansion in bounded-degree graphs. Technical Report TR00-020, Electronic Colloquium on Computational Complexity (ECCC), 2000. Google Scholar
  31. Clement C. (https://math.stackexchange.com/users/75808/clement c). Tail bounds for maximum of sub-gaussian random variables. Mathematics Stack Exchange, 2023. URL:https://math.stackexchange.com/q/4002713 (version: 2023-12-21). URL: https://arxiv.org/abs/https://math.stackexchange.com/q/4002713.
  32. Shiva Prasad Kasiviswanathan, Homin K. Lee, Kobbi Nissim, Sofya Raskhodnikova, and Adam Smith. What can we learn privately? SIAM J. Comput., 40(3):793-826, 2011. URL: https://doi.org/10.1137/090756090.
  33. Shiva Prasad Kasiviswanathan, Homin K. Lee, Kobbi Nissim, Sofya Raskhodnikova, and Adam D. Smith. What can we learn privately? SIAM J. Comput., 40(3):793-826, 2011. URL: https://doi.org/10.1137/090756090.
  34. Ryan O'Donnell. Analysis of Boolean functions. Cambridge University Press, New York, 2014. URL: https://doi.org/10.1017/CBO9781139814782.
  35. Liam Paninski. A coincidence-based test for uniformity given very sparsely sampled discrete data. IEEE Transactions on Information Theory, 54(10):4750-4755, 2008. URL: https://doi.org/10.1109/TIT.2008.928987.
  36. Or Sheffet. Locally private hypothesis testing. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 4612-4621, Stockholmsmässan, Stockholm Sweden, 10-15 July 2018. PMLR. URL: http://proceedings.mlr.press/v80/sheffet18a.html.
  37. Berrett Thomas and Butucea Cristina. Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms. In Proceedings of the 34th International Conference on Neural Information Processing Systems, NIPS '20, pages 3164-3173, Red Hook, NY, USA, 2020. Curran Associates Inc. Google Scholar
  38. Stanley L. Warner. Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60(309):63-69, 1965. URL: https://doi.org/10.1080/01621459.1965.10480775.
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