Advertisement

Distributed Private Heavy Hitters

  • Justin Hsu
  • Sanjeev Khanna
  • Aaron Roth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)

Abstract

In this paper, we give efficient algorithms and lower bounds for solving the heavy hitters problem while preserving differential privacy in the fully distributed local model. In this model, there are n parties, each of which possesses a single element from a universe of size N. The heavy hitters problem is to find the identity of the most common element shared amongst the n parties. In the local model, there is no trusted database administrator, and so the algorithm must interact with each of the n parties separately, using a differentially private protocol. We give tight information-theoretic upper and lower bounds on the accuracy to which this problem can be solved in the local model (giving a separation between the local model and the more common centralized model of privacy), as well as computationally efficient algorithms even in the case where the data universe N may be exponentially large.

Keywords

Hash Function Local Model Full Version Sparse Recovery Heavy Hitter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    McSherry, F., Talwar, K.: Mechanism design via differential privacy. In: Proceedings of the 48th Annual Symposium on Foundations of Computer Science (2007)Google Scholar
  2. 2.
    Gilbert, A., Li, Y., Porat, E., Strauss, M.: Approximate sparse recovery: optimizing time and measurements. In: Proceedings of the 42nd ACM Symposium on Theory of Computing, pp. 475–484. ACM (2010)Google Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Dwork, C.: Differential Privacy: A Survey of Results. In: Agrawal, M., Du, D.-Z., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 1–19. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Kasiviswanathan, S., Lee, H., Nissim, K., Raskhodnikova, S., Smith, A.: What Can We Learn Privately? In: IEEE 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008, pp. 531–540 (2008)Google Scholar
  6. 6.
    Beimel, A., Nissim, K., Omri, E.: Distributed Private Data Analysis: Simultaneously Solving How and What. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 451–468. Springer, Heidelberg (2008)Google Scholar
  7. 7.
    Gupta, A., Hardt, M., Roth, A., Ullman, J.: Privately Releasing Conjunctions and the Statistical Query Barrier. In: Proceedings of the 43rd annual ACM Symposium on the Theory of Computing. ACM, New York (2011)Google Scholar
  8. 8.
    McGregor, A., Mironov, I., Pitassi, T., Reingold, O., Talwar, K., Vadhan, S.: The limits of two-party differential privacy. In: Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 81–90. IEEE (2010)Google Scholar
  9. 9.
    Dwork, C., Naor, M., Pitassi, T., Rothblum, G., Yekhanin, S.: Pan-private streaming algorithms. In: Proceedings of ICS (2010)Google Scholar
  10. 10.
    Mir, D., Muthukrishnan, S., Nikolov, A., Wright, R.: Pan-private algorithms via statistics on sketches. In: Proceedings of the 30th Symposium on Principles of Database Systems of Data, pp. 37–48. ACM (2011)Google Scholar
  11. 11.
    Blum, A., Ligett, K., Roth, A.: A learning theory approach to non-interactive database privacy. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 609–618. ACM (2008)Google Scholar
  12. 12.
    Blum, A., Roth, A.: Fast private data release algorithms for sparse queries. CoRR, abs/1111.6842 (2011)Google Scholar
  13. 13.
    Dwork, C., McSherry, F., Talwar, K.: The price of privacy and the limits of LP decoding. In: Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, p. 94. ACM (2007)Google Scholar
  14. 14.
    Li, Y., Zhang, Z., Winslett, M., Yang, Y.: Compressive mechanism: Utilizing sparse representation in differential privacy. In: Proceedings of the 10th Annual ACM Workshop on Privacy in the Electronic Society, pp. 177–182. ACM (2011)Google Scholar
  15. 15.
    Hsu, J., Khanna, S., Roth, A.: Distributed private heavy hitters. Arxiv preprint arXiv:1202.4910 (2012)Google Scholar
  16. 16.
    Dinur, I., Nissim, K.: Revealing information while preserving privacy. In: 22nd ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS 2003), pp. 202–210 (2003)Google Scholar
  17. 17.
    Beimel, A., Kasiviswanathan, S., Nissim, K.: Bounds on the sample complexity for private learning and private data release. Theory of Cryptography, 437–454 (2010)Google Scholar
  18. 18.
    Hardt, M., Talwar, K.: On the Geometry of Differential Privacy. In: The 42nd ACM Symposium on the Theory of Computing, STOC 2010 (2010)Google Scholar
  19. 19.
    Gupta, A., Ligett, K., McSherry, F., Roth, A., Talwar, K.: Differentially Private Combinatorial Optimization. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Justin Hsu
    • 1
  • Sanjeev Khanna
    • 1
  • Aaron Roth
    • 1
  1. 1.University of PennsylvaniaPhiladelphiaUSA

Personalised recommendations