Differentially Private Filtering

By Jerome Le Ny, George Pappas. 2012

387 citations recorded by the source corpus.

Emerging systems such as smart grids or intelligent transportation systems often require end-user applications to continuously send information to external data aggregators performing monitoring or control tasks. This can result in an undesirable loss of privacy for the users in exchange of the benefits provided by the application. Motivated by this trend, this paper introduces privacy concerns in a system theoretic context, and addresses the problem of releasing filtered signals that respect the privacy of the user data streams. Our approach relies on a formal notion of privacy from the database literature, called differential privacy, which provides strong privacy guarantees against adversaries with arbitrary side information. Methods are developed to approximate a given filter by a differentially private version, so that the distortion introduced by the privacy mechanism is minimized. Two specific scenarios are considered. First, the notion of differential privacy is extended to dynamic systems with many participants contributing independent input signals. Kalman filtering is also discussed in this context, when a released output signal must preserve differential privacy for the measured signals or state trajectories of the individual participants. Second, differentially private mechanisms are described to approximate stable filters when participants contribute to a single event stream, extending previous work on differential privacy under continual observation.

Subfields: Artificial Intelligence

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Citations in the corpus

Differentially Private Distributed Convex Optimization via Functional Perturbation (2015, positive): “Proof: First, note that although a slightly different definition of differential privacy is used in [26], the exact same proof of [26, Theorem 1] works with Definition III.”
Privacy preserving average consensus (2014, background): “In [14], the authors consider the design of differentially private filters for dynamical system by adding white Gaussian perturbations to the system.”
Differentially private cloud-based multi-agent optimization with constraints (2015, methodology): “When computations are performed using this algorithm, noises are added in accordance with the framework for differentially private dynamic systems set forth in [15] in order provide the guarantee of privacy.”
Entropy-minimizing mechanism for differential privacy of discrete-time linear feedback systems (2014, background): “The common approach is to first defining a threshold c > 0 and then calling the two states x1,x2 ∈ R adjacent if ‖x1 − x2‖ ≤ c [2], [3].”
Randomized Iterative Methods for Linear Systems: Momentum, Inexactness and Gossip (2019, methodology): “The last technique is inspired by the addition of noise proposed in [101, 142, 123, 124] for the synchronous setting.”
Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design (2015, neutral): “O C ] 2 8 Fe b 20 17 et al., 2012, 2014, Wang et al., 2014], estimation [Ny and Pappas, 2014], and optimization [Han et al., 2014, Huang et al., 2015, Nozari et al., 2017].”
Stochastic gradient descent with differentially private updates (2013, methodology): “Signal processing methods for differential privacy have recently been investigated by Le Ny and Pappas [9], [10].”
Differentially private iterative synchronous consensus (2012, background): “In the recent paper [18], the authors develop a notion of differential privacy which ensures that an adversary cannot tell the exact input to a dynamical system by looking at its output stream.”
Differentially private Kalman filtering (2012, positive): “In contrast, differential privacy is a worst-case notion that holds independently of any probabilistic assumption on the dataset, and controls the information leakage against adversaries with arbitrary side information [6].”
Differentially Private Distributed Constrained Optimization (2014, background): “It has been reported that certain Netflix subscribers can be identified from the anonymized Netflix prize dataset through auxiliary information from the Intert Movie Database (IMDb) [20].”