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Differentially Private Anomaly Detection for Interconnected Systems

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Safety, Security and Privacy for Cyber-Physical Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 486))

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Abstract

Detecting anomalies in large-scale distributed systems, such as cyber-attacks launched against intelligent transportation systems and other critical infrastructures, or epidemics spreading in human populations, requires the collection and processing of privacy-sensitive data from individuals, such as location traces or medical records. Differential privacy is a powerful theoretical tool that by applying so-called randomized mechanisms to individual data, allows to do meaningful computations at the population level whose results are insensitive, in a probabilistic sense, to the data of any given individual. So far, differential privacy has been applied to several control problems, such as distributed optimization and estimation, filtering and anomaly detection. Still, several issues are open, regarding the balance between the accuracy of the computation results and the guaranteed privacy level for the individuals, as well as the dependence of this balance on the type of randomized mechanism used and on where, in the data acquisition and processing pipeline, the noise is applied. In this chapter, we explore the possibility of using differentially private mechanisms to develop fault-detection algorithms with privacy guarantees and discuss the resulting trade-offs between detection performance and privacy level.

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Notes

  1. 1.

    We stress that while \(\alpha \) is the desired value of the probability of Type I errors, which is used in the design of the threshold, \(P_I\) denotes the actual value. The two are the same as long as the agent \(\mathcal {L}\)’s knowledge of the model of \(\mathcal {S}\) and of the mean and covariance of the uncertainty terms appearing there are correct as stated in Assumptions 10.1 and 10.2.

  2. 2.

    In the literature, the quantity \(1-\beta \) is also termed the probability of Type II errors and denoted as \(P_{II}\), or equivalently the expected Missed Detection Rate (MDR, see [12]).

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Author information

Authors and Affiliations

  1. Delft University of Technology, Delft, The Netherlands

    Riccardo M. G. Ferrari

  2. Polytechnique Montreal and GERAD, Montreal, QC, H3T1J4, Canada

    Kwassi H. Degue & Jerome Le Ny

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  1. Riccardo M. G. Ferrari
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  2. Kwassi H. Degue
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  3. Jerome Le Ny
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Correspondence to Riccardo M. G. Ferrari .

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Editors and Affiliations

  1. Center for Systems and Control, Delft University of Technology, Delft, The Netherlands

    Riccardo M.G. Ferrari

  2. Department of Electrical Engineering, Uppsala University, Uppsala, Sweden

    André M. H. Teixeira

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Ferrari, R.M.G., Degue, K.H., Le Ny, J. (2021). Differentially Private Anomaly Detection for Interconnected Systems. In: Ferrari, R.M., Teixeira, A.M.H. (eds) Safety, Security and Privacy for Cyber-Physical Systems. Lecture Notes in Control and Information Sciences, vol 486. Springer, Cham. https://doi.org/10.1007/978-3-030-65048-3_10

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