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On the measurement complexity of differentially private query answering

差分隐私的测量复杂度研究

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Abstract

Differentially private query answering is an important problem in machine learning and data analysis. As an example, the users may want to know the empirical errors of some classifiers on a training data set which contains sensitive information. In this case, the answers returned by the database holder must preserve privacy. Previous results show that answering large number of queries with differential privacy is computationally expensive. However, almost all the hardness results are conditional, which means that they rely on unproved conjectures. One exception is the hardness for stateless mechanisms, in which the sanitizer is assumed to have very limited memory and can only answer the queries separately. In this work, we explore the hardness for differentially private query answering mechanisms beyond the stateless restriction. Specifically, we investigate the measurement complexity of a natural class of stateful sanitizer. Here, measurement refers to the evaluation of a query (a Boolean function) on a data point. Measurement complexity is a lower bound for the running time. We prove unconditional subexponential lower bound for the measurement complexity of the class of sanitizer with ɛ-differential privacy. Possible generalization of the results is also discussed.

抽象

创新点

差分隐私的计算复杂度. 通过定义并研究所谓测量复杂度, 对于一大类算法 (包括目前已知的差分隐私算法) 给出了不基于其它未证明猜想的复杂度下界. 指出了对于任意算法差分隐私的测量复杂度下界与 P vs NP 问题的关系.

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Authors and Affiliations

  1. Key Laboratory of Machine Perception (MOE), School of Electronics Engineering and Computer Science, Peking University, Beijing, 100871, China

    LiWei Wang

  2. Computer Science and Engineering Department, University of California, San Diego, CA, 92093, USA

    JiaPeng Zhang

Authors
  1. LiWei Wang
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  2. JiaPeng Zhang
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Correspondence to LiWei Wang.

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Wang, L., Zhang, J. On the measurement complexity of differentially private query answering. Sci. China Inf. Sci. 58, 1–11 (2015). https://doi.org/10.1007/s11432-015-5306-x

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  • DOI: https://doi.org/10.1007/s11432-015-5306-x

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