Skip to main content
SpringerLink
Log in

Efficient Discrete Distribution Estimation Schemes Under Local Differential Privacy

  • Conference paper
  • First Online:
Frontiers in Cyber Security (FCS 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1286))

Included in the following conference series:

Abstract

Recently, local differential privacy (LDP) has increasingly been leveraged to cope with privacy issues in data collection. Discrete distribution estimation schemes under LDP are the fundamental tools in the LDP setting, which enable data collector to collect discrete distribution estimation information about a population while protecting each individual’s privacy, without relying on a trusted third party. Among these schemes, Ye-Barg mechanisms achieve the best utility in the medium privacy regime. Nevertheless, their communication cost between the user and data collector is O(k) which is too large to be deployed in practice when the domain size k is large (or even unbounded). In this paper, we propose a family of new efficient discrete distribution estimation schemes under LDP which reduce the communication cost to less than \(O(\mathrm {log}(2+e^\epsilon ))\) and obtain almost the same expected estimation loss as Ye-Barg mechanisms under \(\ell _2^2\) metric and \(\ell _1\) metric. Additionally, we compare our schemes with Ye-Barg mechanisms theoretically and experimentally and confirm our conclusion.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Dwork, C.: Differential privacy: a survey of results. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 1–19. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-79228-4_1

    Chapter  MATH  Google Scholar 

  2. Chen, R., Li, H., Qin, A.K., Kasiviswanathan, S.P., Jin, H.: Private spatial data aggregation in the local setting. In: 2016 IEEE 32nd International Conference on Data Engineering (ICDE), pp. 289–300. IEEE, Helsinki (2016)

    Google Scholar 

  3. Kasiviswanathan, S.P., Lee, H.K., Nissim, K., Raskhodnikova, S., Smith, A.: What can we learn privately? In: 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 531–540. IEEE, Philadelphia (2008)

    Google Scholar 

  4. Kasiviswanathan, S.P., Lee, H.K., Nissim, K., Raskhodnikova, S., Smith, A.: What can we learn privately? SIAM J. Comput. 2(3), 793–826 (2011)

    Article  MathSciNet  Google Scholar 

  5. Erlingsson, Ú., Pihur, V., Korolova, A.: RAPPOR: randomized aggregatable privacy-preserving ordinal response. In: Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, pp. 1054–1067. ACM, New York (2014)

    Google Scholar 

  6. Fanti, G., Pihur, V., Erlingsson, Ú.: Building a RAPPOR with the unknown: privacy-preserving learning of associations and data dictionaries. Proc. Priv. Enhanc. Technol. 2016(3), 41–61 (2016)

    Article  Google Scholar 

  7. Cormode, G., Jha, S., Kulkarni, T., Li, N., Srivastava, D., Wang, T.: Privacy at scale: local differential privacy in practice. In: Proceedings of the 2018 International Conference on Management of Data, pp. 1655–1658. ACM, New York (2018)

    Google Scholar 

  8. Ding, B., Kulkarni, J., Yekhanin, S.: Collecting telemetry data privately. In: Advances in Neural Information Processing Systems, pp. 3571–3580. Curran Associates, New York (2017)

    Google Scholar 

  9. Wang, T., et al.: Answering multi-dimensional analytical queries under local differential privacy. In: Proceedings of the 2019 International Conference on Management of Data, pp. 159–176. ACM, New York (2019)

    Google Scholar 

  10. Bassily, R., Smith, A.: Local, private, efficient protocols for succinct histograms. In: Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, pp. 127–135. ACM, New York (2015)

    Google Scholar 

  11. Wang, S., et al.: Mutual information optimally local private discrete distribution estimation. arXiv preprint arXiv:1607.08025 (2016)

  12. Holohan, N., Leith, D.J., Mason, O.: Optimal differentially private mechanisms for randomised response. IEEE Trans. Inf. Forensics Secur. 12(11), 2726–2735 (2017)

    Article  Google Scholar 

  13. Wang, T., Blocki, J., Li, N., Jha, S.: Locally differentially private protocols for frequency estimation. In: 26th USENIX Security Symposium, pp. 729–745. ACM, New York (2017)

    Google Scholar 

  14. Ye, M., Barg, A.: Optimal schemes for discrete distribution estimation under locally differential privacy. IEEE Trans. Inf. Theory 64(8), 5662–5676 (2018)

    Article  MathSciNet  Google Scholar 

  15. Bassily, R., Nissim, K., Stemmer, U., Thakurta, A.G.: Practical locally private heavy hitters. In: Advances in Neural Information Processing Systems, pp. 2288–2296. Curran Associates, New York (2017)

    Google Scholar 

  16. Krishnan, S., Wang, J., Franklin, M.J., Goldberg, K., Kraska, T.: PrivateClean: data cleaning and differential privacy. In: Proceedings of the 2016 International Conference on Management of Data, pp. 937–951. ACM, New York (2016)

    Google Scholar 

  17. Dwork, C., McSherry, F., Nissim, K., Smith, A.: Calibrating noise to sensitivity in private data analysis. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 265–284. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_14

    Chapter  Google Scholar 

  18. McSherry, F., Talwar, K.: Mechanism design via differential privacy. In: 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2007), pp. 94–103. IEEE, Providence (2007)

    Google Scholar 

  19. Dwork, C., Roth, A.: The algorithmic foundations of differential privacy. Found. Trends Theor. Comput. Sci. 9(3–4), 211–407 (2014)

    MathSciNet  MATH  Google Scholar 

  20. Wang, T., Li, N., Jha, S.: Locally differentially private heavy hitter identification. IEEE Trans. Dependable Secure Comput. (2019). https://doi.org/10.1109/TDSC.2019.2927695

    Article  Google Scholar 

  21. Qin, Z., Yang, Y., Yu, T., Khalil, I., Xiao, X., Ren, K.: Heavy hitter estimation over set-valued data with local differential privacy. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 192–203. ACM, New York (2016)

    Google Scholar 

  22. Cormode, G., Kulkarni, T., Srivastava, D.: Answering range queries under local differential privacy. Proc. VLDB Endow. 12(10), 1126–1138 (2019)

    Article  Google Scholar 

  23. Qardaji, W., Yang, W., Li, N.: Understanding hierarchical methods for differentially private histograms. Proc. VLDB Endow. 6(14), 1954–1965 (2013)

    Article  Google Scholar 

  24. Xiao, X., Wang, G., Gehrke, J.: Differential privacy via wavelet transforms. IEEE Trans. Knowl. Data Eng. 23(8), 1200–1214 (2010)

    Article  Google Scholar 

  25. Xue, Q., Zhu, Y., Wang, J., Li, X., Zhang, J.: Distributed set intersection and union with local differential privacy. In: 2017 IEEE 23rd International Conference on Parallel and Distributed Systems (ICPADS), Shenzhen, pp. 198–205 (2017)

    Google Scholar 

  26. Xue, Q., Zhu, Y., Wang, J.: Joint distribution estimation and Naïve Bayes classification under local differential privacy. IEEE Trans. Emerg. Top. Comput. (2019). https://doi.org/10.1109/TETC.2019.2959581

    Article  Google Scholar 

  27. Balle, B., Wang, Y.X.: Improving the Gaussian mechanism for differential privacy: analytical calibration and optimal denoising. arXiv preprint arXiv:1805.06530 (2018)

  28. Duchi, J.C., Jordan, M.I., Wainwright, M.J.: Minimax optimal procedures for locally private estimation. J. Am. Stat. Assoc. 113(521), 182–201 (2018)

    Article  MathSciNet  Google Scholar 

  29. Wang, N., et al.: Collecting and analyzing multidimensional data with local differential privacy. In: 2019 IEEE 35th International Conference on Data Engineering (ICDE), pp. 638–649. IEEE, Macao (2019)

    Google Scholar 

  30. Sangaiah, A.K., Medhane, D.V., Han, T., Hossain, M.S., Muhammad, G.: Enforcing position-based confidentiality with machine learning paradigm through mobile edge computing in real-time industrial informatics. IEEE Trans. Ind. Inf. 15(7), 4189–4196 (2019)

    Article  Google Scholar 

  31. Sangaiah, A.K., Medhane, D.V., Bian, G.B., Ghoneim, A., Alrashoud, M., Hossain, M.S.: Energy-aware green adversary model for cyberphysical security in industrial system. IEEE Trans. Ind. Inf. 16(5), 3322–3329 (2019)

    Article  Google Scholar 

Download references

Acknowledgment

This work is partly supported by the National Key Research and Development Program of China (No.2017YFB0802300), and the Research Fund of Guangxi Key Laboratory of Trusted Software (No. kx201906).

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Wenlong Dun & Youwen Zhu

  2. Guangxi Key Laboratory of Trusted Software, Guilin University of Electronic Technology, Guilin, 541004, China

    Youwen Zhu

Authors
  1. Wenlong Dun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Youwen Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Youwen Zhu .

Editor information

Editors and Affiliations

  1. Tianjin University, Tianjin, China

    Guangquan Xu

  2. Delft University of Technology, Delft, The Netherlands

    Kaitai Liang

  3. University of Aizu, Aizuwakamatsu, Japan

    Chunhua Su

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dun, W., Zhu, Y. (2020). Efficient Discrete Distribution Estimation Schemes Under Local Differential Privacy. In: Xu, G., Liang, K., Su, C. (eds) Frontiers in Cyber Security. FCS 2020. Communications in Computer and Information Science, vol 1286. Springer, Singapore. https://doi.org/10.1007/978-981-15-9739-8_38

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-9739-8_38

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-9738-1

  • Online ISBN: 978-981-15-9739-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation