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Differentially private histogram publication

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Abstract

Differential privacy (DP) is a promising scheme for releasing the results of statistical queries on sensitive data, with strong privacy guarantees against adversaries with arbitrary background knowledge. Existing studies on differential privacy mostly focus on simple aggregations such as counts. This paper investigates the publication of DP-compliant histograms, which is an important analytical tool for showing the distribution of a random variable, e.g., hospital bill size for certain patients. Compared to simple aggregations whose results are purely numerical, a histogram query is inherently more complex, since it must also determine its structure, i.e., the ranges of the bins. As we demonstrate in the paper, a DP-compliant histogram with finer bins may actually lead to significantly lower accuracy than a coarser one, since the former requires stronger perturbations in order to satisfy DP. Moreover, the histogram structure itself may reveal sensitive information, which further complicates the problem. Motivated by this, we propose two novel mechanisms, namely NoiseFirst and StructureFirst, for computing DP-compliant histograms. Their main difference lies in the relative order of the noise injection and the histogram structure computation steps. NoiseFirst has the additional benefit that it can improve the accuracy of an already published DP-compliant histogram computed using a naive method. For each of proposed mechanisms, we design algorithms for computing the optimal histogram structure with two different objectives: minimizing the mean square error and the mean absolute error, respectively. Going one step further, we extend both mechanisms to answer arbitrary range queries. Extensive experiments, using several real datasets, confirm that our two proposals output highly accurate query answers and consistently outperform existing competitors.

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Notes

  1. http://www.ncbi.nlm.nih.gov/gap.

  2. http://www.moh.gov.sg/content/moh_web/home/statistics.html.

  3. An alternative definition of sensitivity [9] concerns the maximum changes in the query results after modifying a record in the database. In our example, this leads to \(\Delta =2\), since in the worst case, changing a person’s age can affect the values in two different bins by 1 each.

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Acknowledgments

Jia Xu and Ge Yu are supported by the National Basic Research Program of China (973) under Grant 2012CB316201, the National Natural Science Foundation of China (with Nos. 61033007 and 61003058), and the Fundamental Research Funds for the Central Universities (with No. N100704001). Zhenjie Zhang and Yin Yang are supported by SERC Grant No. 102 158 0074 from Singapore’s A*STAR. Xiaokui Xiao is supported by Nanyang Technological University under SUG Grant M58020016 and AcRF Tier 1 Grant RG 35/09, and by the Agency for Science, Technology and Research (Singapore) under SERG Grant 1021580074

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Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, China

    Jia Xu & Ge Yu

  2. Advanced Digital Sciences Center, Illinois at Singapore Pte. Ltd, Singapore, Singapore

    Zhenjie Zhang & Yin Yang

  3. School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    Xiaokui Xiao

  4. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA

    Marianne Winslett

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  1. Jia Xu
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  2. Zhenjie Zhang
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  3. Xiaokui Xiao
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  4. Yin Yang
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  5. Ge Yu
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Correspondence to Ge Yu.

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Xu, J., Zhang, Z., Xiao, X. et al. Differentially private histogram publication. The VLDB Journal 22, 797–822 (2013). https://doi.org/10.1007/s00778-013-0309-y

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