The price of privacy and the limits of LP decoding

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2007, Pages 85-94

  Dwork, Cynthia ^a   McSherry, Frank ^a   Talwar, Kunal ^a  

^a MICROSOFT RESEARCH   (United States)

Author keywords

Basis pursuit; Compressed sensing; LP decoding; Privacy

Indexed keywords

BASIS PURSUIT; COMPRESSED SENSING; LP DECODING;

DATABASE SYSTEMS; ERROR ANALYSIS; GAUSSIAN DISTRIBUTION; LINEAR PROGRAMMING; STATISTICAL METHODS;

COMPUTER PRIVACY;

EID: 35449000081     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1250790.1250804     Document Type: Conference Paper

References (25)

1. D. Achlioptas. Database-friendly random projections: Johnson- Lindenstrauss with binary coins. J. Comput. Syst. Sci., 66(4):671-687, 2003.
2. A. Blum, C. Dwork, F. McSherry, and K. Nissim. Practical privacy: the sulq framework. In C. Li, editor, PODS, pages 128-138. ACM, 2005.
3. E. J. Candès, M. Rudelson, T. Tao, and R. Vershynin. Error correction via linear programming. In FOCS, pages 295-308. IEEE Computer Society, 2005.
4. E. J. Candès and T. Tao. Decoding by linear programming. IEEE Transactions on Information Theory, 51(12):4203-4215, 2005.
5. E. J. Candes and T. Tao. Error correction via linear programming, 2005.
6. E. J. Cands and P. Randall. Highly robust error correction by convex programming. Submitted, 2006.
7. S. Chen, D. Donoho, and M. Saunders. Atomic decomposition by basis pursuit. SIAM J. Sci Comp, 48(1):33-61, 1999.
8. I. Dinur, C. Dwork, and K. Nissim. Privacy in public databases: A foundational approach, 2005. Manuscript.
9. I. Dinur and K. Nissim. Revealing information while preserving privacy. In PODS, pages 202-210. ACM, 2003.
10. D. Donoho. For most large underdetermined systems of linear equations, the minimal 11-norm near-solution approximates the sparsest near-solution. Communications on Pure and Applied Mathematics, 59(7):907-934, 2006.
11. D. Donoho. For most large underdetermined systems of linear equations, the minimal 11-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics, 59(6):797-829, 2006.
12. D. Donoho. High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension. Discrete and Computational Geometry, 35(4):617-652, 2006.
13. D. Donoho and X. Huo. Uncertainty principles and ideal atomic decomposition. IEEE Transactions on Information Theory, 48:2845-2862, 2001.
14. D. Donoho and I. M. Johnstone. Minimax estimation via wavelet shrinkage. Annals of Statistics, 26(3):879-921, 1998.
15. D. Donoho and J. Tanner. Thresholds for the recovery of sparse solutions via l1 minimization. In Proceedings of the Conference on Information Sciences and Systems, 2006.
16. D. L. Donoho. Compressed sensing. IEEE Transactions on Information Theory, 52(4): 1289-1306, 2006.
17. C. Dwork, F. McSherry, K. Nissim, and A. Smith. Calibrating noise to sensitivity in private data analysis. In S. Halevi and T. Rabin, editors, TCC, volume 3876 of Lecture Notes in Computer Science, pages 265-284. Springer, 2006.
18. C. Dwork and K. Nissim. Privacy-preserving datamining on vertically partitioned databases. In M. K. Franklin, editor, CRYPTO, volume 3152 of Lecture Notes in Computer Science, pages 528-544. Springer, 2004.
19. J. Feldman. Decoding error-correcting codes via linear programming. Master's thesis, Massachusetts Institute of Technology, 2003.
20. J. Feldman and D. Karger. Decoding turbo-like codes via linear programming. Journal of Computer and System Sciences, 68(4):733-752, 2004.
21. J. Feldman, T. Malkin, C. Stein, R. Servedio, and M. Wainwright. LP decoding corrects a constant fraction of errors (an expanded version). In ISIT, pages 68-. IEEE, 2004.
22. J. Feldman and C. Stein. LP decoding achieves capacity. In SODA, pages 460-469. SIAM, 2005.
23. 1 bounds in normal approximation. Annals of Probability, 2006. To Appear.
24. M. Ledoux. The Concentration of Measure Phenomenon, volume 89 of Mathematical Surveys and Monographs. American Mathematical Society, 2001.
25. M. Talagrand. Concentration of measure and isoperimetric inequalities in product space. Publ. Math I.H.E.S., 81:73-205, 1995.