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Locating a Small Cluster Privately

Published:15 June 2016Publication History

ABSTRACT

We present a new algorithm for locating a small cluster of points with differential privacy [Dwork, McSherry, Nissim, and Smith, 2006]. Our algorithm has implications to private data exploration, clustering, and removal of outliers. Furthermore, we use it to significantly relax the requirements of the sample and aggregate technique [Nissim, Raskhodnikova, and Smith, 2007], which allows compiling of "off the shelf" (non-private) analyses into analyses that preserve differential privacy.

References

  1. P. K. Agarwal, S. Har-Peled, and K. R. Varadarajan. Geometric approximation via coresets. In COMBINATORIAL AND COMPUTATIONAL GEOMETRY, MSRI, pages 1--30. University Press, 2005.Google ScholarGoogle Scholar
  2. R. Bassily, K. Nissim, A. D. Smith, T. Steinke, U. Stemmer, and J. Ullman. Algorithmic stability for adaptive data analysis. STOC (to appear), 2016. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. A. Beimel, K. Nissim, and U. Stemmer. Private learning and sanitization: Pure vs. approximate differential privacy. In APPROX-RANDOM, volume 8096 of Lecture Notes in Computer Science, pages 363--378. Springer, 2013.Google ScholarGoogle ScholarCross RefCross Ref
  4. M. Bun, K. Nissim, U. Stemmer, and S. P. Vadhan. Differentially private release and learning of threshold functions. In FOCS, pages 634--649, 2015. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. C. Dwork, V. Feldman, M. Hardt, T. Pitassi, O. Reingold, and A. L. Roth. Preserving statistical validity in adaptive data analysis. In STOC, pages 117--126. ACM, 2015. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. C. Dwork, K. Kenthapadi, F. McSherry, I. Mironov, and M. Naor. Our data, ourselves: Privacy via distributed noise generation. In S. Vaudenay, editor, EUROCRYPT, volume 4004 of Lecture Notes in Computer Science, pages 486--503. Springer, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. C. Dwork and J. Lei. Differential privacy and robust statistics. In M. Mitzenmacher, editor, STOC, pages 371--380. ACM, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. C. Dwork, F. McSherry, K. Nissim, and A. Smith. Calibrating noise to sensitivity in private data analysis. In TCC, volume 3876 of Lecture Notes in Computer Science, pages 265--284. Springer, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. C. Dwork, M. Naor, O. Reingold, G. N. Rothblum, and S. P. Vadhan. On the complexity of differentially private data release: efficient algorithms and hardness results. In M. Mitzenmacher, editor, STOC, pages 381--390. ACM, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. C. Dwork, G. N. Rothblum, and S. P. Vadhan. Boosting and differential privacy. In FOCS, pages 51--60. IEEE Computer Society, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. W. B. Johnson and J. Lindenstrauss. Extensions of Lipschitz maps into a Hilbert space. 1984.Google ScholarGoogle Scholar
  12. S. P. Kasiviswanathan, H. K. Lee, K. Nissim, S. Raskhodnikova, and A. Smith. What can we learn privately? SIAM J. Comput., 40(3):793--826, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. B. Laurent and P. Massart. Adaptive estimation of a quadratic functional by model selection. Ann. Statist., 28(5):1302--1338, 10 2000.Google ScholarGoogle ScholarCross RefCross Ref
  14. F. McSherry and K. Talwar. Mechanism design via differential privacy. In FOCS, pages 94--103. IEEE Computer Society, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. P. Mohan, A. Thakurta, E. Shi, D. Song, and D. E. Culler. GUPT: privacy preserving data analysis made easy. In Proceedings of the ACM SIGMOD International Conference on Management of Data, SIGMOD 2012, Scottsdale, AZ, USA, May 20--24, 2012, pages 349--360, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. K. Nissim, S. Raskhodnikova, and A. Smith. Smooth sensitivity and sampling in private data analysis. In STOC, pages 75--84. ACM, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. V. Shenmaier. The problem of a minimal ball enclosing k points. Journal of Applied and Industrial Mathematics, 7(3):444--448, 2013.Google ScholarGoogle ScholarCross RefCross Ref
  18. A. Smith. Privacy-preserving statistical estimation with optimal convergence rates. In Proceedings of the 43rd ACM Symposium on Theory of Computing, STOC 2011, San Jose, CA, USA, 6--8 June 2011, pages 813--822, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. A. Thakurta and A. Smith. Differentially private feature selection via stability arguments, and the robustness of the lasso. In S. Shalev-Shwartz and I. Steinwart, editors, COLT, volume 30 of JMLR Proceedings, pages 819--850. JMLR.org, 2013.Google ScholarGoogle Scholar
  20. S. Vadhan. The Complexity of Differential Privacy. 2016.Google ScholarGoogle Scholar

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      • Published in

        cover image ACM Conferences
        PODS '16: Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems
        June 2016
        504 pages
        ISBN:9781450341912
        DOI:10.1145/2902251
        • General Chair:
        • Tova Milo,
        • Program Chair:
        • Wang-Chiew Tan

        Copyright © 2016 ACM

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        Publication History

        • Published: 15 June 2016

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        PODS '16 Paper Acceptance Rate31of94submissions,33%Overall Acceptance Rate642of2,707submissions,24%

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