Abstract
The methodology of differential privacy has provided a strong definition of privacy which in some settings, using a mechanism of doubly-exponential noise addition, also allows for extraction of informative statistics from databases. A recent paper extends this approach to the release of a specified set of margins from a multi-way contingency table. Privacy protection in such settings implicitly focuses on small cell counts that might allow for the identification of units that are unique in the database. We explore how well the mechanism works in the context of a series of examples, and the extent to which the proposed differential-privacy mechanism allows for sensible inferences from the released data.
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References
Barak, B., Chaudhuri, K., Dwork, C., Kale, S., McSherry, F., Talwar, K.: Privacy, accuracy, and consistency too: A holistic solution to contingency table release. In: Proceedings of the 26th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (2007)
Bishop, Y.M., Fienberg, S.E., Holland, P.W.: Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge (1975); reprinted: Springer (2007)
Christiansen, S.K., Giese, H.: Genetic analysis of obligate barley powdery mildew fungus based on rfpl and virulence loci. Theoretical and Applied Genetics 79, 705–712 (1991)
Dobra, A., Fienberg, S.E., Rinaldo, A., Slavkovic, A.B., Zhou, Y.: Algebraic statistics and contingency table problems: Log-linear models, likelihood estimation, and disclosure limitation. In: Putinar, M., Sullivant, S. (eds.) Emerging Applications of Algebraic Geometry. IMA Series in Applied Mathematics, pp. 63–88. Springer, Heidelberg (2008)
Duncan, G.T., Fienberg, S.E., Krishnan, R., Padman, R., Roehrig, S.F.: Disclosure limitation methods and information loss for tabular data. In: Doyle, P., Lane, J., Theeuwes, J., Zayatz, L. (eds.) Confidentiality, Disclosure and Data Access: Theory and Practical Applications for Statistical Agencies, pp. 135–166. Elsevier, Amsterdam (2001)
Dwork, C.: Differential privacy. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 1–12. Springer, Heidelberg (2006)
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)
Edwards, D.: Linkage analysis using log-linear models. Comp. Statist. and Data Anal. 13, 281–290 (1992)
Edwards, D.: Introduction to Graphical Modelling, 2nd edn. Springer, Heidelberg (2000)
Edwards, D., Havranek, T.: Fast procedure for model search in multidimensional contingency tables. Biometrika 72, 339–351 (1985)
Fienberg, S.E., Slavkovic, A.B.: A survey of statistical approaches to preserving confi- dentiality of contingency table entries. In: Aggarwal, C., Yu, P.S. (eds.) Privacy Preserving Data Mining: Models and Algorithms, pp. 289–310. Springer, Heidelberg (2008)
Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford (1996)
Wasserman, L., Shuheng, Z.: A statistical framework for differential privacy. J. Amer. Statist. Assoc. 105, 375–389 (2010)
Whittaker, J.: Graphical Models in Applied Multivariate Statistics. Wiley, Chichester (1990)
Winkler, W.: General Discret-data Modeling Methods for Producing Synthetic Data with Reduced Re-identification Risk that Preserve Analytic Properties. Research Report Series, Statistics 2010-02 (2008)
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Fienberg, S.E., Rinaldo, A., Yang, X. (2010). Differential Privacy and the Risk-Utility Tradeoff for Multi-dimensional Contingency Tables. In: Domingo-Ferrer, J., Magkos, E. (eds) Privacy in Statistical Databases. PSD 2010. Lecture Notes in Computer Science, vol 6344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15838-4_17
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DOI: https://doi.org/10.1007/978-3-642-15838-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15837-7
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