Differential privacy for symbolic systems with application to Markov Chains

Chen, Bin; Leahy, Kevin; Jones, Adam G.; Hale, Matthew

doi:10.1016/j.automatica.2023.110908

Cited by 12 publications

(2 citation statements)

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“…Two differentially private gradient methods were proposed for distributed optimization problems in [33] to ensure both privacy and optimization accuracy. For some non-numerical or symbolic data, a novel differential privacy mechanism was proposed in [34] for protecting sensitive symbolic system trajectories and the results were applied to Markov chains. From the point of systems and control theory, the authors in [35] investigated the relation between differential privacy and strong input observability of the systems and designed a privacy-preserving controller for a tracking problem.…”

Section: Introductionmentioning

confidence: 99%

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Privacy Preservation of Nabla Discrete Fractional-Order Dynamic Systems

Ma,

Hu,

Peng

2024

Fractal Fract

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This article investigates the differential privacy of the initial state for nabla discrete fractional-order dynamic systems. A novel differentially private Gaussian mechanism is developed which enhances the system’s security by injecting random noise into the output state. Since the existence of random noise gives rise to the difficulty of analyzing the nabla discrete fractional-order systems, to cope with this challenge, the observability of nabla discrete fractional-order systems is introduced, establishing a connection between observability and differential privacy of initial values. Based on it, the noise magnitude required for ensuring differential privacy is determined by utilizing the observability Gramian matrix of systems. Furthermore, an optimal Gaussian noise distribution that maximizes algorithmic performance while simultaneously ensuring differential privacy is formulated. Finally, a numerical simulation is provided to validate the effectiveness of the theoretical analysis.

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Section: Introductionmentioning

confidence: 99%

“…(Necessity). Suppose the system is observable, then x 0 can be uniquely determined from the system of Equation (34). The system yields a unique solution for x 0 , which means there exists at least n rows in O L that are linearly independent.…”

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confidence: 99%