ABSTRACT
This work presents a mechanism to debias polynomial functions computed from locally differentially private data. Local differential privacy is a widely used privacy notion where users add Laplacian noise to their information before submitting it to a central server. That, however, causes bias when we calculate non-linear functions based on those noisy information. Our proposed recursive algorithm debiases these functions, with a calculation time of O(r n log n), where r is the polynomial degree and n is the number of users. We evaluate our method on the problems of k-star counting and variance estimation, comparing results with state-of-the-art algorithms. The results show that our method not only eliminates bias, but also provides at least 100 times more accuracy than previous works.
Supplemental Material
- Alain Barrat and Martin Weigt. 2000. On the properties of small-world network models. The European Physical Journal B-Condensed Matter and Complex Systems, 13, 3, 547--560.Google ScholarCross Ref
- Graham Cormode, Somesh Jha, Tejas Kulkarni, Ninghui Li, Divesh Srivastava, and Tianhao Wang. 2018. Privacy at scale: Local differential privacy in practice. In Proceedings of the 2018 International Conference on Management of Data, 1655--1658.Google ScholarDigital Library
- John C. Duchi, Michael I. Jordan, and Martin J. Wainwright. 2018. Minimax optimal procedures for locally private estimation. Journal of the American Statistical Association, 113, 521, 182--201.Google ScholarCross Ref
- Cynthia Dwork. 2008. Differential privacy: A survey of results. In Theory and Applications of Models of Computation: 5th International Conference (TAMC 2008). Springer, Xi'an, China, (Apr. 2008), 1--19.Google ScholarCross Ref
- Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith. 2006. Calibrating noise to sensitivity in private data analysis. In Theory of Cryptography: Third Theory of Cryptography Conference (TCC 2006). Springer, New York, NY, USA, (Mar. 2006), 265--284.Google ScholarDigital Library
- Úlfar Erlingsson, Vasyl Pihur, and Aleksandra Korolova. 2014. Rappor: Randomized aggregatable privacy-preserving ordinal response. In Proceedings of the 2014 ACM SIGSAC conference on computer and communications security, 1054--1067.Google ScholarDigital Library
- Giulia Fanti, Vasyl Pihur, and Úlfar Erlingsson. 2015. Building a RAPPOR with the unknown: privacy-preserving learning of associations and data dictionaries. arXiv:1503.01214.Google Scholar
- Michael Hay, Chao Li, Gerome Miklau, and David Jensen. 2009. Accurate estimation of the degree distribution of private networks. In 2009 Ninth IEEE International Conference on Data Mining. IEEE, 169--178.Google ScholarDigital Library
- Jacob Imola, Takao Murakami, and Kamalika Chaudhuri. 2021. Locally differentially private analysis of graph statistics. In 30st USENIX Security Symposium (USENIX Security 21), 983--1000.Google Scholar
- Jacob Imola, Takao Murakami, and Kamalika Chaudhuri. 2022. Communication-Efficient Triangle Counting under Local Differential Privacy. In 31st USENIX Security Symposium (USENIX Security 22). Boston, MA, 537--554.Google Scholar
- Honglu Jiang, Jian Pei, Dongxiao Yu, Jiguo Yu, Bei Gong, and Xiuzhen Cheng. 2021. Applications of differential privacy in social network analysis: a survey. IEEE Transactions on Knowledge and Data Engineering.Google ScholarCross Ref
- Zach Jorgensen, Ting Yu, and Graham Cormode. 2015. Conservative or liberal? Personalized differential privacy. In 2015 IEEE 31st International Conference on Data Engineering (ICDE). IEEE, Seoul, South Korea, (Apr. 2015), 1023--1034. isbn: 978-1-4799-7964-6. doi: 10.1109/ICDE.2015.7113353.Google ScholarCross Ref
- Shiva Prasad Kasiviswanathan, Homin K. Lee, Kobbi Nissim, Sofya Raskhodnikova, and Adam Smith. 2011. What can we learn privately? SIAM Journal on Computing, 40, 3, 793--826.Google ScholarDigital Library
- Tomasz J. Kozubowski and Saralees Nadarajah. 2010. Multitude of Laplace distributions. Statistical Papers, 51, 1, 127--148.Google ScholarCross Ref
- Russell W. F. Lai, Giulio Malavolta, and Dominique Schröder. 2018. Homomorphic Secret Sharing for Low Degree Polynomials. In Advances in Cryptology: 24th International Conference on the Theory and Application of Cryptology and Information Securit (ASIACRYPT 2018). Springer International Publishing, Brisbane, QLD, Australia, (Dec. 2018), 279--309. isbn: 978-3-030-03332-3.Google Scholar
- Jure Leskovec and Andrej Krevl. 2014. SNAP Datasets: Stanford large network dataset collection. (2014). http://snap.stanford.edu/data.Google Scholar
- Zitao Li, Tianhao Wang, Milan Lopuhaä-Zwakenberg, Ninghui Li, and Boris koric. 2020. Estimating numerical distributions under local differential privacy. In Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data, 621--635.Google ScholarDigital Library
- Naurang S. Mangat. 1994. An improved randomized response strategy. Journal of the Royal Statistical Society: Series B (Methodological), 56, 1, 93--95.Google ScholarCross Ref
- University of Limerick. 2005. 12th annual graph drawing contest. (2005). http: //mozart.diei.unipg.it/gdcontest/contest2005/index.html.Google Scholar
- Kittiphop Phalakarn, Vorapong Suppakitpaisarn, Nuttapong Attrapadung, and Kanta Matsuura. 2020. Constructive t-secure homomorphic secret sharing for low degree polynomials. In Progress in Cryptology: 21st International Conference on Cryptology in India (INDOCRYPT 2020). Springer, Bangalore, India, (Dec. 2020), 763--785.Google ScholarDigital Library
- Zhan Qin, Ting Yu, Yin Yang, Issa Khalil, Xiaokui Xiao, and Kui Ren. 2017. Generating synthetic decentralized social graphs with local differential privacy. In Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, 425--438.Google ScholarDigital Library
- Ning Wang, Xiaokui Xiao, Yin Yang, Ta Duy Hoang, Hyejin Shin, Junbum Shin, and Ge Yu. 2018. PrivTrie: Effective frequent term discovery under local differential privacy. In 34th International Conference on Data Engineering (ICDE). IEEE, 821--832.Google ScholarCross Ref
- Zhibo Wang, Jiahui Hu, Ruizhao Lv, Jian Wei, Qian Wang, Dejun Yang, and Hairong Qi. 2019. Personalized Privacy-Preserving Task Allocation for Mobile Crowdsensing. IEEE Transactions on Mobile Computing, 18, 6, (June 2019), 1330--1341. doi: 10.1109/TMC.2018.2861393.Google ScholarDigital Library
- Stanley L. Warner. 1965. Randomized response: A survey technique for elimi- nating evasive answer bias. Journal of the American Statistical Association, 60, 309, 63--69.Google ScholarCross Ref
- Duncan J. Watts and Steven H. Strogatz. 1998. Collective dynamics of small-world'networks. Nature, 393, 6684, 440--442.Google Scholar
- Akito Yamamoto, Eizen Kimura, and Tetsuo Shibuya. 2023. (ε, k)-Randomized Anonymization: ε-Differentially Private Data Sharing with k-Anonymity. In Proceedings of the 16th International Conference on Health Informatics (HEALTH-INF 2023). Lisbon, Portugal.Google ScholarCross Ref
- Ying Zhao and Jinjun Chen. 2022. A survey on differential privacy for unstructured data content. ACM Computing Surveys (CSUR), 54, 10s, 1--28.Google Scholar
- Keyu Zhu, Pascal Van Hentenryck, and Ferdinando Fioretto. 2021. Bias and Variance of Post-processing in Differential Privacy. In Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. (May 2021), 11177--11184. doi: 10.1609/aaai.v35i12.17333.Google ScholarCross Ref
- Tianqing Zhu, Gang Li, Wanlei Zhou, and S. Yu Philip. 2017. Differentially private data publishing and analysis: A survey. IEEE Transactions on Knowledge and Data Engineering, 29, 8, 1619--1638. Publisher: IEEE.Google ScholarDigital Library
Index Terms
- Unbiased Locally Private Estimator for Polynomials of Laplacian Variables
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