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We study the (nearly) optimal mechanisms in $(\epsilon,\delta)$-approximate differential privacy for integer-valued query functions and vector-valued (histogram-like) query functions under a utility-maximization/cost-minimization framework.
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C. Dwork, K. Kenthapadi, F. McSherry, I. Mironov, and M. Naor, “Our data, ourselves: Privacy via distributed noise generation,” in Proceedings of the 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques , ser. EUROCRYPT ’06. Berlin, Heidelberg: Springer-Verlag, 2006, pp. 486–503
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K. Chaudhuri and N. Mishra, “When random sampling preserves privacy,” in Proceedings of the 26th annual international conference on Advances in Cryptology , ser. CRYPTO’06. Berlin, Heidelberg: Springer-Verlag, 2006, pp. 198–213
2006
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K. Nissim, S. Raskhodnikova, and A. Smith, “Smooth sensitivity and sampling in private data analysis,” in Proceedings of the Thirty-Ninth annual ACM Symposium on Theory of Computing , ser. STOC ’07. New York, NY, USA: ACM, 2007, pp. 75–84
2007
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F. McSherry and K. Talwar, “Mechanism design via differential privacy,” in Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science , ser. FOCS ’07. Washington, DC, USA: IEEE Computer Society, 2007, pp. 94–103
2007
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C. Dwork, “Differential privacy: A survey of results,” in Proceedings of the 5th International Conference on Theory and Applications of Models of Computation , ser. TAMC’08. Berlin, Heidelberg: Springer-Verlag, 2008, pp. 1–19
2008
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2008
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A. Machanavajjhala, D. Kifer, J. Abowd, J. Gehrke, and L. Vilhuber, “Privacy: Theory meets practice on the map,” in Proceedings of the 2008 IEEE 24th International Conference on Data Engineering , ser. ICDE ’08. Washington, DC, USA: IEEE Computer Society, 2008, pp. 277–286
2008
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C. Dwork and J. Lei, “Differential privacy and robust statistics,” in Proceedings of the 41st Annual ACM symposium on Theory of Computing , ser. STOC ’09. New York, NY, USA: ACM, 2009, pp. 371–380
2009
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A. Ghosh, T. Roughgarden, and M. Sundararajan, “Universally utility-maximizing privacy mechanisms,” in Proceedings of the 41st Annual ACM Symposium on Theory of Computing , ser. STOC ’09. New York, NY, USA: ACM, 2009, pp. 351–360
2009
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C. Dwork, G. N. Rothblum, and S. Vadhan, “Boosting and differential privacy,” in Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science , ser. FOCS ’10. Washington, DC, USA: IEEE Computer Society, 2010, pp. 51–60
2010
Cited alongside, same era.
S. P. Kasiviswanathan, M. Rudelson, A. Smith, and J. Ullman, “The price of privately releasing contingency tables and the spectra of random matrices with correlated rows,” in Proceedings of the 42nd ACM Symposium on Theory of Computing , ser. STOC ’10. New York, NY, USA: ACM, 2010, pp. 775–784
2010
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H. Brenner and K. Nissim, “Impossibility of differentially private universally optimal mechanisms,” in Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science , ser. FOCS ’10, Oct. 2010, pp. 71 –80
Q. Geng and P. Viswanath, “The optimal mechanism in differential privacy,” ArXiv e-prints , Dec. 2012
2012
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A. De, “Lower bounds in differential privacy,” in Proceedings of the 9th International Conference on Theory of Cryptography , ser. TCC’12. Berlin, Heidelberg: Springer-Verlag, 2012, pp. 321–338
2012
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C. Fang and E.-C. Chang, “Adaptive differentially private histogram of low-dimensional data,” in Privacy Enhancing Technologies , ser. Lecture Notes in Computer Science, S. Fischer-Hübner and M. Wright, Eds. Springer Berlin Heidelberg, 2012, vol. 7384, pp. 160–179
2012
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J. Xu, Z. Zhang, X. Xiao, Y. Yang, and G. Yu, “Differentially private histogram publication,” in 2012 IEEE 28th International Conference on Data Engineering (ICDE) . IEEE, 2012, pp. 32–43
2012
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2010
Cited alongside, same era.
M. Gupte and M. Sundararajan, “Universally optimal privacy mechanisms for minimax agents,” in Symposium on Principles of Database Systems , 2010, pp. 135–146
2010
Cited alongside, same era.
M. Hay, V. Rastogi, G. Miklau, and D. Suciu, “Boosting the accuracy of differentially private histograms through consistency,” Proceedings of the VLDB Endowment , vol. 3, no. 1-2, pp. 1021–1032, Sep. 2010
2010
Cited alongside, same era.
M. Hardt and K. Talwar, “On the geometry of differential privacy,” in Proceedings of the 42nd ACM Symposium on Theory of Computing , ser. STOC ’10. New York, NY, USA: ACM, 2010, pp. 705–714
2010
Cited alongside, same era.
C. Li, M. Hay, V. Rastogi, G. Miklau, and A. McGregor, “Optimizing linear counting queries under differential privacy,” in Proceedings of the Twenty-Ninth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems , ser. PODS ’10. New York, NY, USA: ACM, 2010, pp. 123–134
2010
Cited alongside, same era.
2010
Cited alongside, same era.
P. Jain, P. Kothari, and A. Thakurta, “Differentially private online learning,” in Proceedings of the 25th Annual Conference on Learning Theory , ser. COLT ’12, 2012
2012
Later among the works it cites.
——, “The optimal mechanism in differential privacy: Multidimensional setting,” ArXiv e-prints , Dec. 2013
2013
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A. Nikolov, K. Talwar, and L. Zhang, “The geometry of differential privacy: The sparse and approximate cases,” in Proceedings of the 45th Annual ACM Symposium on Symposium on Theory of Computing , ser. STOC ’13. New York, NY, USA: ACM, 2013, pp. 351–360
2013
Closest in time.
R. Hall, A. Rinaldo, and L. Wasserman, “Differential privacy for functions and functional data,” Journal of Machine Learning Research , vol. 14, pp. 703–727, 2013
2013
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S. Oh and P. Viswanath, “The composition theorem for differential privacy,” ArXiv e-prints , Nov. 2013
2013
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