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Publishing Set-Valued Data via Differential Privacy Rui Chen, Concordia University Noman Mohammed, Concordia University Benjamin C. M. Fung, Concordia University Bipin C. Desai, Concordia University Li Xiong, Emory University 1 VLDB 2011

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Outline Introduction Preliminaries Sanitization algorithm Experimental results Conclusions 2

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Introduction The problem: non-interactive set-valued data publication under differential privacy 3 Typical set-valued data: transaction data, web search queries

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Introduction Set-valued data refers to the data in which each record owner is associated with a set of items drawn from an item universe. 4 TIDItems t1 I1, I2, I3, I4 t2 I2, I4 t3 I2 t4 I1, I2 t5 I2 t6 I1 t7 I1, I2, I3, I4 t8 I2, I3, I4

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Introduction Existing works [1, 2, 3, 4, 5, 6, 7] on publishing set-valued data are based on partitioned-based privacy models [8]. They provide insufficient privacy protection. – Composition attack [8] – deFinetti attack [9] – Foreground knowledge attack [10] They are vulnerable to background knowledge. 5

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Introduction Differential privacy is independent of an adversary’ background knowledge and computational power (with exceptions [11]). The outcome of any analysis should not overly depend on a single data record. Existing differentially private data publishing approaches are not adequate in terms of both utility and scalability for our problem. 6

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Introduction Problems of data-independent publishing approaches: 7 Universe I = {I 1, I 2, I 3 } I1 I2 I3 I1, I2 I1, I3 I2, I3 I1, I2, I3 Scalability: O(2 n ) Utility: noise accumulates exponentially

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Outline Introduction Preliminaries Sanitization algorithm Experimental results Conclusions 8

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Preliminaries Context-free taxonomy tree 9 Each internal node is a set of their leaves, not necessarily the semantic generalization

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Preliminaries Differential privacy [12] 10 A non-interactive privacy mechanism A gives ε-differential privacy if for all neighbours D, D’, and for any possible sanitized database D* ∈ Range(A), Pr A [A(D) = D*] ≤ exp(ε) × Pr A [A(D’) = D*] DD’ D and D’ are neighbors if they differ on at most one record

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Preliminaries Laplace mechanism [12] 11 For example, for a single counting query Q over a dataset D, returning Q(D)+Laplace(1/ε) gives ε-differential privacy. Global Sensitivity

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Preliminaries Exponential mechanism [13] 12 Given a utility function q : (D × R) → R for a database instance D, the mechanism A, A(D, q) = { return r with probability ∝ exp(ε×q(D, r)/2 △ q) } gives ε-differential privacy.

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Preliminaries Composition properties [14] 13 Sequential composition ∑ i ε i –differential privacy Parallel composition max(ε i )–differential privacy

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Preliminaries Utility metrics 14 For a given itemset I’ I, a counting query Q over a dataset D is defined to be A privacy mechanism A is (α, δ)-useful if with probability 1- δ, for every counting query and every dataset D, for D*=A(D), |Q(D*)-Q(D)|<= α. [15]

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Outline Introduction Preliminaries Sanitization algorithm Experimental results Conclusions 15

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Sanitization Algorithm Top-down partitioning 16 Generalize all records to a single partition Keep partitioning non-empty partitions until leaf partitions are reached TIDItems t1 I1, I2, I3, I4 t2 I2, I4 t3 I2 t4 I1, I2 t5 I2 t6 I1 t7 I1, I2, I3, I4 t8 I2, I3, I4

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Sanitization Algorithm Privacy budget allocation 17 We reserve B/2 to obtain noisy sizes of leaf partitions and the rest B/2 to guide the partitioning. Assign less budget to more general partitions and more budget to more specific partitions.

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Sanitization Algorithm Privacy budget allocation 18 Example: {I {1,2}, I {3, 4} } needs at most two partition operations to reach leaf partitions A hierarchy cut needs at most partition operations to reach leaf partitions.

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Sanitization Algorithm Privacy budget allocation 19 We reserve B/2 to obtain noisy sizes of leaf partitions and the rest B/2 to guide the partitioning. Assign less budget to more general partitions and more budget to more specific partitions. B/2/3 = B/6 (B/2-B/6)/2 = B/6 B/6+B/2 = 2B/3

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Sanitization Algorithm Sub-partition generation 20 For a non-leaf partition, we need to consider all possible sub-partitions to satisfy differential privacy. Efficient implementation: separately handling empty and non-empty partitions (inspired by [16]).

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Outline Introduction Preliminaries Sanitization algorithm Experimental results Conclusions 21

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Experiments Two real-life set-valued datasets are used. 22 MSNBC is publicly available at UCI machine learning repository(http://archive.ics.uci.edu/ml/index.html). STM is provided by Societe de transport de Montreal (STM) (http://www.stm.info).

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Experiments Average relative error vs. privacy budget 23 B=0.5 B=0.75 B=1.0

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Experiments Utility for frequent itemset mining 24 B=0.5 B=0.75 B=1.0

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Experiments Scalability: O(|D|*|I|) 25 Runtime vs. |D|Runtime vs. |I|

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Outline Introduction Preliminaries Sanitization algorithm Experimental results Conclusions 26

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Conclusions Differential privacy can be successfully applied to non- interactive set-valued data publishing with guaranteed utility. Differential privacy can be achieved by data-dependent solutions with improved efficiency and accuracy. The general idea of data-dependent solutions applies to other types of data, for example, relational data [17] and trajectory data [18]. 27

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References [1] J. Cao, P. Karras, C. Raissi, and K.-L. Tan. ρ–uncertainty inference proof transaction anonymization. In VLDB, pp. 1033–1044, 2010. [2] G. Ghinita, Y. Tao, and P. Kalnis. On the anonymization of sparse high-dimensional data. In ICDE, pp. 715–724, 2008. [3] Y. He and J. F. Naughton. Anonymization of set-valued data via top-down, local generalization. In VLDB, pp. 934–945, 2009. [4] M. Terrovitis, N. Mamoulis, and P. Kalnis. Privacy-preserving anonymization of set- valued data. In VLDB, pp.115–125, 2008. [5] M. Terrovitis, N. Mamoulis, and P. Kalnis. Local and global recoding methods for anonymizing set-valued data.VLDBJ, 20(1):83–106, 2011. [6] Y. Xu, B. C. M. Fung, K. Wang, A. W. C. Fu, and J. Pei. Publishing sensitive transactions for itemset utility. In ICDM, pp. 1109–1114, 2008. [7] Y. Xu, K. Wang, A. W. C. Fu, and P. S. Yu. Anonymizing transaction databases for publication. In SIGKDD, pp. 767–775, 2008. 28

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References [8] S. R. Ganta, S. P. Kasiviswanathan, and A. Smith. Composition attacks and auxiliary information in data privacy. In SIGKDD, pp. 265-273, 2008. [9] D. Kifer. Attacks on privacy and deFinetti’s theorem. In SIGMOD, pp. 127–138, 2009. [10] R. C. W. Wong, A. Fu, K. Wang, P. S. Yu, and J. Pei. Can the utility of anonymized data be used for privacy breaches,” ACM Transactions on Knowledge Discovery from Data, to appear. [11] D. Kifer and A. Machanavajjhala. No free lunch in data privacy. In SIGMOD, 2011. [12] C. Dwork, F. McSherry, K. Nissim, and A. Smith. Calibrating noise to sensitivity in private data analysis. In Theory of Cryptography Conference, pp. 265–284, 2006. [13] F. McSherry and K. Talwar. Mechanism design via differential privacy. In FOCS, pp. 94–103, 2007. [14] F. McSherry. Privacy integrated queries: An extensible platform for privacy- preserving data analysis. In SIGMOD, pp. 19–30, 2009. [15] A. Blum, K. Ligett, and A. Roth. A learning theory approach to non-interactive database privacy. In STOC, pp.609–618, 2008. 29

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References [16] G. Cormode, M. Procopiuc, D. Srivastava, and T. T. L. Tran. Differentially Private Publication of Sparse Data. In CoRR, 2011. [17] N. Mohammed, R. Chen, B. C. M. Fung, and P. S. Yu. Differentially private data release for data mining. In SIGKDD, 2011. [18] R. Chen, B. C. M. Fung, and B. C. Desai. Differentially private trajectory data publication. ICDE, under review, 2012. 30

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Thank you! Q & A 31

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Backup Slides 32

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Lower Bound Results In the interactive setting, only a limited number of queries could be answered; otherwise, an adversary would be able to precisely reconstruct almost the entire original database. In the non-interactive setting, one can only guarantee the utility of restricted classes of queries. 33

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Threshold Selection We design the threshold as a function of the standard deviation of the noise and the height of a partition’s hierarchy cut: 36

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Relative error (α, δ)-usefulness is effective to give an overall estimation of utility, but fails to produce intuitive experimental results. We experimentally measure the utility of sanitized data for counting queries by relative error: 37 Sanity bound

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Experiments Average relative error vs. taxonomy tree fan-out 38 B=0.5 B=0.75 B=1.0

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