On Linear Refinement of Differential Privacy-Preserving Query Answering
Recent work showed the necessity of incorporating a user’s background knowledge to improve the accuracy of estimates from noisy responses of histogram queries. Various types of constraints (e.g., linear constraints, ordering constraints, and range constraints) may hold on the true (non-randomized) answers of histogram queries. So the idea was to apply the constraints over the noisy responses and find a new set of answers (called refinements) that are closest to the noisy responses and also satisfy known constraints. As a result, the refinements expect to boost the accuracy of final histogram query results. However, there is one key question: is the ratio of the distributions of the results after refinements from any two neighbor databases still bounded? In this paper, we introduce a new definition, ρ-differential privacy on refinement, to quantify the change of distributions of refinements. We focus on one representative refinement, the linear refinement with linear constraints and study the relationship between the classic ε-differential privacy ( on responses) and our ρ-differential privacy on refinement. We demonstrate the conditions when the ρ-differential privacy on refinement achieves the same ε-differential privacy. We argue privacy breaches could incur when the conditions do not meet.
Keywordsdifferential privacy linear constraint refinement background knowledge
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- 2.Dwork, C.: A Firm Foundation for Private Data Analysis. Communications of the ACM (January 2011)Google Scholar
- 3.Hay, M., Rastogi, V., Miklau, G., Suciu, D.: Boosting the Accuracy of Differentially Private Histograms Through Consistency. Proceedings of the VLDB Endowment 3(1) (2010)Google Scholar
- 4.Xiao, X., Wang, G., Gehrke, J.: Differential Privacy via Wavelet Transforms. In: Proceedings of the 26th IEEE International Conference on Data Enginering, pp. 225–236. IEEE (2010)Google Scholar
- 5.Li, C., Hay, M., Rastogi, V., Miklau, G., McGregor, A.: Optimizing Linear Counting Queries Under Differential Privacy. In: Proceedings of the 29th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems of Data, pp. 123–134. ACM (2010)Google Scholar
- 6.Dwork, C., Lei, J.: Differential Privacy and Robust Statistics. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, pp. 371–380. ACM (2009)Google Scholar
- 7.Hay, M., Li, C., Miklau, G., Jensen, D.: Accurate Estimation of the Degree Distribution of Private Networks. In: Proceedings of the 9th IEEE International Conference on Data Mining, pp. 169–178. IEEE (2009)Google Scholar
- 8.Martin, D., Kifer, D., Machanavajjhala, A., Gehrke, J., Halpern, J.: Worst-Case Background Knowledge for Privacy-Preserving Data Publishing. In: Proceedings of the 26th IEEE International Conference on Data Enginering. IEEE (2007)Google Scholar
- 9.Du, W., Teng, Z., Zhu, Z.: Privacy-MaxEnt: Integrating Background Knowledge in Privacy Quantification. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, ACM (2008)Google Scholar
- 10.Ganta, S., Kasiviswanathan, S., Smith, A.: Composition Attacks and Auxiliary Information in Data Privacy. In: Proceeding of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 265–273. ACM (2008)Google Scholar
- 11.Kifer, D., Machanavajjhala, A.: No Free Lunch in Data Privacy. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 193–204. ACM (2011)Google Scholar