A Model Randomization Approach to Statistical Parameter Privacy

• Published in: IEEE transactions on automatic control Vol. 68; no. 2; pp. 839 - 850
• Main Authors: Nekouei, Ehsan, Sandberg, Henrik, Skoglund, Mikael, Johansson, Karl Henrik
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bandpass filters; Building automation; Building management systems; Complexity theory; Convex optimization; Convexity; Data privacy; Filter design (mathematics); Filter designs; Filter output; Information theory; Joint probability density function; Kalman filtering; Kalman filters; Kernel; Markov processes; Mathematical transformations; Mutual information; Mutual informations; Non-linear transformations; Numerical prediction; Optimization; Parameter estimation; Parameters; Privacy; privacy in networked control systems; Probability density function; Probability density functions; Randomisation; State estimation; Statistical analysis; Statistical parameters; Structural design; Testing; Transformations (mathematics)
• DOI: 10.1109/TAC.2022.3145664
• ISSN: 0018-9286; 1558-2523

In this article, we study a privacy filter design problem for a sequence of sensor measurements whose joint probability density function (p.d.f.) depends on a private parameter. To ensure parameter privacy, we propose a filter design framework which consists of two components: a randomizer and a nonlinear transformation. The randomizer takes the private parameter as input and randomly generates a pseudo parameter. The nonlinear mapping transforms the measurements such that the joint p.d.f. of the filter's output depends on the pseudo parameter rather than the private parameter. It also ensures that the joint p.d.f. of the filter's output belongs to the same family of distributions as that of the measurements. The design of the randomizer is formulated as an optimization problem subject to a privacy constraint, in terms of mutual information, and it is shown that the optimal randomizer is the solution of a convex optimization problem. Using information-theoretic inequalities, we show that the performance of any estimator of the private parameter, based on the output of the privacy filter, is limited by the privacy constraint. The structure of the nonlinear transformation is studied in the special cases of independent and identically distributed, Markovian, and Gauss-Markov measurements. Our results show that the privacy filter in the Gauss-Markov case can be implemented as two one-step ahead Kalman predictors and a set of minimum mean square error predictors. A numerical example on occupancy privacy in a building automation system illustrates the approach.